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Quadratic Equations Calculator

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1

Here, we show you a step-by-step solved example of quadratic equations. This solution was automatically generated by our smart calculator:

$x^2-1=99$
2

We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $-1$ from both sides of the equation

$x^2-1+1=99+1$

Canceling terms on both sides

$x^2=99-1\cdot -1$

Multiply $-1$ times $-1$

$x^2=99+1$

Add the values $99$ and $1$

$x^2=100$
3

Canceling terms on both sides

$x^2=100$
4

Removing the variable's exponent

$\sqrt{x^2}=\pm \sqrt{100}$
5

Cancel exponents $2$ and $\frac{1}{2}$

$x=\pm \sqrt{100}$
6

The square root of $100$ is

$x=\pm 10$
7

As in the equation we have the sign $\pm$, this produces two identical equations that differ in the sign of the term $10$. We write and solve both equations, one taking the positive sign, and the other taking the negative sign

$x=10,\:x=-10$
8

Combining all solutions, the $2$ solutions of the equation are

$x=10,\:x=-10$

Final answer to the problem

$x=10,\:x=-10$

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