Solve 2-2(2-a^2)=6

$$2 - 2 ( 2 - a ^ { 2 } ) = 6$$

Solve for a

$$a=2$$

$$a=-2$$

Steps Using Difference of Squares

Use the distributive property to multiply -2 by 2-a^{2}.

$$2-4+2a^{2}=6$$

Subtract 4 from 2 to get -2.

$$-2+2a^{2}=6$$

Subtract 6 from both sides.

$$-2+2a^{2}-6=0$$

Subtract 6 from -2 to get -8.

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

Divide both sides by 2.

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

Consider -4+a^{2}. Rewrite -4+a^{2} 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

Use the distributive property to multiply -2 by 2-a^{2}.

$$2-4+2a^{2}=6$$

Subtract 4 from 2 to get -2.

$$-2+2a^{2}=6$$

Add 2 to both sides.

$$2a^{2}=6+2$$

Add 6 and 2 to get 8.

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

Divide both sides by 2.

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

Divide 8 by 2 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

Use the distributive property to multiply -2 by 2-a^{2}.

$$2-4+2a^{2}=6$$

Subtract 4 from 2 to get -2.

$$-2+2a^{2}=6$$

Subtract 6 from both sides.

$$-2+2a^{2}-6=0$$

Subtract 6 from -2 to get -8.

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

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.

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

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

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

Square 0.

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

Multiply -4 times 2.

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

Multiply -8 times -8.

$$a=\frac{0±\sqrt{64}}{2\times 2}$$

Take the square root of 64.

$$a=\frac{0±8}{2\times 2}$$

Multiply 2 times 2.

$$a=\frac{0±8}{4}$$

Now solve the equation a=\frac{0±8}{4} when ± is plus. Divide 8 by 4.

$$a=2$$

Now solve the equation a=\frac{0±8}{4} when ± is minus. Divide -8 by 4.

$$a=-2$$

The equation is now solved.

$$a=2 a=-2$$