Solve 8x^2+4=804

$$8 x ^ { 2 } + 4 = 804$$

Solve for x

$$x=10$$

$$x=-10$$

Steps Using Difference of Squares

Subtract 804 from both sides.

$$8x^{2}+4-804=0$$

Subtract 804 from 4 to get -800.

$$8x^{2}-800=0$$

Divide both sides by 8.

$$x^{2}-100=0$$

Consider x^{2}-100. Rewrite x^{2}-100 as x^{2}-10^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-10\right)\left(x+10\right)=0$$

To find equation solutions, solve x-10=0 and x+10=0.

$$x=10 x=-10$$

Steps by Finding Square Root

Subtract 4 from both sides.

$$8x^{2}=804-4$$

Subtract 4 from 804 to get 800.

$$8x^{2}=800$$

Divide both sides by 8.

$$x^{2}=\frac{800}{8}$$

Divide 800 by 8 to get 100.

$$x^{2}=100$$

Take the square root of both sides of the equation.

$$x=10 x=-10$$

Steps Using the Quadratic Formula

Subtract 804 from both sides.

$$8x^{2}+4-804=0$$

Subtract 804 from 4 to get -800.

$$8x^{2}-800=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -800 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-800\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-800\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-800\right)}}{2\times 8}$$

Multiply -32 times -800.

$$x=\frac{0±\sqrt{25600}}{2\times 8}$$

Take the square root of 25600.

$$x=\frac{0±160}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±160}{16}$$

Now solve the equation x=\frac{0±160}{16} when ± is plus. Divide 160 by 16.

$$x=10$$

Now solve the equation x=\frac{0±160}{16} when ± is minus. Divide -160 by 16.

$$x=-10$$

The equation is now solved.

$$x=10 x=-10$$