Solve 16^2=20^2-left(2x+xright)^2

$${ 16 }^{ 2 } = { 20 }^{ 2 } - { \left(2x+x \right) }^{ 2 }$$

Solve for x

$$x=4$$

$$x=-4$$

Steps by Finding Square Root

Calculate 16 to the power of 2 and get 256.

$$256=20^{2}-\left(2x+x\right)^{2}$$

Calculate 20 to the power of 2 and get 400.

$$256=400-\left(2x+x\right)^{2}$$

Combine 2x and x to get 3x.

$$256=400-\left(3x\right)^{2}$$

Expand \left(3x\right)^{2}.

$$256=400-3^{2}x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$256=400-9x^{2}$$

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

$$400-9x^{2}=256$$

Subtract 400 from both sides.

$$-9x^{2}=256-400$$

Subtract 400 from 256 to get -144.

$$-9x^{2}=-144$$

Divide both sides by -9.

$$x^{2}=\frac{-144}{-9}$$

Divide -144 by -9 to get 16.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

Steps Using the Quadratic Formula

Calculate 16 to the power of 2 and get 256.

$$256=20^{2}-\left(2x+x\right)^{2}$$

Calculate 20 to the power of 2 and get 400.

$$256=400-\left(2x+x\right)^{2}$$

Combine 2x and x to get 3x.

$$256=400-\left(3x\right)^{2}$$

Expand \left(3x\right)^{2}.

$$256=400-3^{2}x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$256=400-9x^{2}$$

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

$$400-9x^{2}=256$$

Subtract 256 from both sides.

$$400-9x^{2}-256=0$$

Subtract 256 from 400 to get 144.

$$144-9x^{2}=0$$

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.

$$-9x^{2}+144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -9 for a, 0 for b, and 144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-9\right)\times 144}}{2\left(-9\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-9\right)\times 144}}{2\left(-9\right)}$$

Multiply -4 times -9.

$$x=\frac{0±\sqrt{36\times 144}}{2\left(-9\right)}$$

Multiply 36 times 144.

$$x=\frac{0±\sqrt{5184}}{2\left(-9\right)}$$

Take the square root of 5184.

$$x=\frac{0±72}{2\left(-9\right)}$$

Multiply 2 times -9.

$$x=\frac{0±72}{-18}$$

Now solve the equation x=\frac{0±72}{-18} when ± is plus. Divide 72 by -18.

$$x=-4$$

Now solve the equation x=\frac{0±72}{-18} when ± is minus. Divide -72 by -18.

$$x=4$$

The equation is now solved.

$$x=-4 x=4$$