High School Math Solutions – Radical Equation Calculator

Radical equations are equations involving radicals of any order.  We will show examples of square roots; higher order radicals simply require more of the same work.   To solve radical equations you first have to get rid of the radicals, in the case of square roots square both sides of the equation (in some cases this should be done multiple times), then refine the new equation (either linear or quadratic) and solve. One more thing to note, by squaring the equation we changed the original equation, so it is very important to check the solutions at the end.

Let’s see how it works, simply follow the steps:
1. Simplify: eliminate the square root
2. Refine: refine the quadratic equation after squaring the root
3. Solve: solve the equation
4. Verify: plug the solutions into the original equation and verify

Click here for an example:

Now let’s zoom in on how to simplify the radical.  You will notice that the first step is to isolate the square root before squaring both sides of the equation:

Here’s a more advanced example that requires multiple steps to resolve the radical (click here):

Cheers,
Michal

Perpendicular Line, Normal Line, Elimination Method, Biquadratic Equations and More

What’s in common between Perpendicular Line, Normal Line, Elimination Method and Bi-quadratic Equations? All are new features we’ve just added.  This calls for a blog post!

So what’s new?  Step by step solutions for Normal line, Perpendicular line, Elimination Method, and Biquadratic Equations, pretty amazing!

Let’s dive right into this:

Perpendicular Line

Perpendicular lines have a negative reciprocal slope, all it takes to find the equation of the line perpendicular to the line at a point is to calculate the slope.

Let’s see how it works (click here):

Normal Line

The normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point.  To find the normal line, find the tangent line first then find the equation of the perpendicular line (same technique as above).  Symbolab knows how to do all this, type Normal (along with the function and point), and Go.

Here’s how it looks like (click here):

System of Equations – Elimination Method

The Elimination Method is the process of eliminating one of the variables in a system of equations using addition or subtraction.  The Substitution Method is the process of solving an equation for one variable, and subsequently substituting that solution in the other equation.  In most cases you can use one or the other.

We’ve made it easier for you to select the method of your choice.  Type in the system of equations, press Go, you should notice the different methods listed.

Click here to see how it works:

Simply click “Using the elimination method” to get the solution steps by elimination:

Bi-quadratic Equations

A bi-quadratic equation is a quadratic function of a square, having the form f(x)=ax^4+bx^2+c. To solve you simply have to rewrite the equation as a quadratic equation.

Here’s how Symbolab does just that (click here):

Enjoy the new features!

Cheers,
Michal

High School Math Solutions – Quadratic Equations Calculator, Part 3

On the last post we covered completing the square (see link).  It is pretty strait forward if you follow all the steps (there are quite a few steps).

To make things simple, a general formula can be derived such that for a quadratic equation of the form ax²+bx+c=0 the solutions are x=(-b ± sqrt(b^2-4ac))/2a. The quadratic formula comes in handy, all you need to do is to plug in the coefficients and the constants (a,b and c). One thing to note, you must memorize the formula, it is not as intuitive as factoring or completing the square.

Let’s see how it works (click here):

Here’s an advanced example that involves complex numbers (click here):

We’ve got you covered; that was the last on the Quadratic Equations series. Now you know everything there is to know about solving quadratic equations.

Cheers,
Michal

High School Math Solutions – Quadratic Equations Calculator, Part 2

Solving quadratics by factorizing (link to previous post) usually works just fine.  But what if the quadratic equation can’t be factored, you're going to need a different strategy to help you solve it.

An equation in which one side is a perfect square trinomial can be easily solved by taking the square root of each side.  Easy is good, so we basically want to force the quadratic equation into the form (x+a)²=x²+2ax+a².

All it takes is making sure that the coefficient of the highest power (x²) is one.  Move the constant term to the right hand side.  Take half of the coefficient of the middle term(x), square it, and add that value to both sides of the equation.  Factor the perfect square trinomial.  Take the square root of each side and solve.

With practice you will get the hang of it.

Let’s see how it works (click here):

Here’s another example (click here):

Until next time,
Michal

High School Math Solutions – Quadratic Equations Calculator, Part 1

A quadratic equation is a second degree polynomial having the general form ax^2 + bx + c = 0, where a, b, and c are constants.

We will look at three different methods for solving quadratics: factorization, completing the square, and the quadratic formula.   Symbolab is using all three methods, simply click the [+] next to the method of your choice to see the detailed solution steps.

Here’s how it looks like (click here to see on symbolab):

First up is factorization.

How do you factorize a quadratic? Use the Symbolab solutions technique that we saw in the middle school math solutions edition  (To access Symbolab Factoring Calculator click here).

The trick is to get the equation to the form (x-u)(x-v)=0, now we have to solve much simpler equations (any number multiplied by zero equals zero ).

Let’s see how it works (click here):

Here’s another example just to get the hang of it (click here):

Until next time,
Michal