Solve 8x^2-200=0

$$8 x ^ { 2 } - 200 = 0$$

Solve for x

$$x=5$$

$$x=-5$$

Steps Using Difference of Squares

Divide both sides by 8.

$$x^{2}-25=0$$

Consider x^{2}-25. Rewrite x^{2}-25 as x^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-5\right)\left(x+5\right)=0$$

To find equation solutions, solve x-5=0 and x+5=0.

$$x=5 x=-5$$

Steps by Finding Square Root

Add 200 to both sides. Anything plus zero gives itself.

$$8x^{2}=200$$

Divide both sides by 8.

$$x^{2}=\frac{200}{8}$$

Divide 200 by 8 to get 25.

$$x^{2}=25$$

Take the square root of both sides of the equation.

$$x=5 x=-5$$

Steps Using the Quadratic Formula

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.

$$8x^{2}-200=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-200\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-200\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-200\right)}}{2\times 8}$$

Multiply -32 times -200.

$$x=\frac{0±\sqrt{6400}}{2\times 8}$$

Take the square root of 6400.

$$x=\frac{0±80}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±80}{16}$$

Now solve the equation x=\frac{0±80}{16} when ± is plus. Divide 80 by 16.

$$x=5$$

Now solve the equation x=\frac{0±80}{16} when ± is minus. Divide -80 by 16.

$$x=-5$$

The equation is now solved.

$$x=5 x=-5$$