Solve 144=16+x^2

$$144=16+ { x }^{ 2 }$$

Solve for x

$$x=8\sqrt{2}\approx 11.313708499$$

$$x=-8\sqrt{2}\approx -11.313708499$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$16+x^{2}=144$$

Subtract 16 from both sides.

$$x^{2}=144-16$$

Subtract 16 from 144 to get 128.

$$x^{2}=128$$

Take the square root of both sides of the equation.

$$x=8\sqrt{2} x=-8\sqrt{2}$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$16+x^{2}=144$$

Subtract 144 from both sides.

$$16+x^{2}-144=0$$

Subtract 144 from 16 to get -128.

$$-128+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-128=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -128 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-128\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-128\right)}}{2}$$

Multiply -4 times -128.

$$x=\frac{0±\sqrt{512}}{2}$$

Take the square root of 512.

$$x=\frac{0±16\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±16\sqrt{2}}{2} when ± is plus.

$$x=8\sqrt{2}$$

Now solve the equation x=\frac{0±16\sqrt{2}}{2} when ± is minus.

$$x=-8\sqrt{2}$$

The equation is now solved.

$$x=8\sqrt{2} x=-8\sqrt{2}$$