Solve 8a^2-32=0

$$8 a ^ { 2 } - 32 = 0$$

Solve for a

$$a=2$$

$$a=-2$$

Steps Using Difference of Squares

Divide both sides by 8.

$$a^{2}-4=0$$

Consider a^{2}-4. Rewrite a^{2}-4 as a^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(a-2\right)\left(a+2\right)=0$$

To find equation solutions, solve a-2=0 and a+2=0.

$$a=2 a=-2$$

Steps by Finding Square Root

Add 32 to both sides. Anything plus zero gives itself.

$$8a^{2}=32$$

Divide both sides by 8.

$$a^{2}=\frac{32}{8}$$

Divide 32 by 8 to get 4.

$$a^{2}=4$$

Take the square root of both sides of the equation.

$$a=2 a=-2$$

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.

$$8a^{2}-32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 8\left(-32\right)}}{2\times 8}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 8\left(-32\right)}}{2\times 8}$$

Multiply -4 times 8.

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

Multiply -32 times -32.

$$a=\frac{0±\sqrt{1024}}{2\times 8}$$

Take the square root of 1024.

$$a=\frac{0±32}{2\times 8}$$

Multiply 2 times 8.

$$a=\frac{0±32}{16}$$

Now solve the equation a=\frac{0±32}{16} when ± is plus. Divide 32 by 16.

$$a=2$$

Now solve the equation a=\frac{0±32}{16} when ± is minus. Divide -32 by 16.

$$a=-2$$

The equation is now solved.

$$a=2 a=-2$$