Solve 816=880-4x^2

$$816 = 880 - 4 x ^ { 2 }$$

Solve for x

$$x=4$$

$$x=-4$$

Steps by Finding Square Root

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

$$880-4x^{2}=816$$

Subtract 880 from both sides.

$$-4x^{2}=816-880$$

Subtract 880 from 816 to get -64.

$$-4x^{2}=-64$$

Divide both sides by -4.

$$x^{2}=\frac{-64}{-4}$$

Divide -64 by -4 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

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

$$880-4x^{2}=816$$

Subtract 816 from both sides.

$$880-4x^{2}-816=0$$

Subtract 816 from 880 to get 64.

$$64-4x^{2}=0$$

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.

$$-4x^{2}+64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 0 for b, and 64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 64}}{2\left(-4\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4\right)\times 64}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$x=\frac{0±\sqrt{16\times 64}}{2\left(-4\right)}$$

Multiply 16 times 64.

$$x=\frac{0±\sqrt{1024}}{2\left(-4\right)}$$

Take the square root of 1024.

$$x=\frac{0±32}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{0±32}{-8}$$

Now solve the equation x=\frac{0±32}{-8} when ± is plus. Divide 32 by -8.

$$x=-4$$

Now solve the equation x=\frac{0±32}{-8} when ± is minus. Divide -32 by -8.

$$x=4$$

The equation is now solved.

$$x=-4 x=4$$