Solve By Extracting Square Root a. x ^ 2 = 144 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\left. \begin{array} { l } { x ^ { 2 } = 144 } \end{array} \right.$$

Solve for x

$x=12$
$x=-12$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Subtract $144$ from both sides.

$$x^{2}-144=0$$

Consider $x^{2}-144$. Rewrite $x^{2}-144$ as $x^{2}-12^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(x-12\right)\left(x+12\right)=0$$

To find equation solutions, solve $x-12=0$ and $x+12=0$.

$$x=12$$ $$x=-12$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=12$$ $$x=-12$$

Steps Using the Quadratic Formula

Subtract $144$ from both sides.

$$x^{2}-144=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-144$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-144\right)}}{2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-144\right)}}{2}$$

Multiply $-4$ times $-144$.

$$x=\frac{0±\sqrt{576}}{2}$$

Take the square root of $576$.

$$x=\frac{0±24}{2}$$

Now solve the equation $x=\frac{0±24}{2}$ when $±$ is plus. Divide $24$ by $2$.

$$x=12$$

Now solve the equation $x=\frac{0±24}{2}$ when $±$ is minus. Divide $-24$ by $2$.

$$x=-12$$

The equation is now solved.

$$x=12$$ $$x=-12$$