Solve 7=-(x-2)(x+2)

$$7 = - ( x - 2 ) ( x + 2 )$$

Solve for x (complex solution)

$$x=-\sqrt{3}i\approx -0-1.732050808i$$

$$x=\sqrt{3}i\approx 1.732050808i$$

Steps by Finding Square Root

To find the opposite of x-2, find the opposite of each term.

$$7=\left(-x-\left(-2\right)\right)\left(x+2\right)$$

The opposite of -2 is 2.

$$7=\left(-x+2\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of -x+2 by each term of x+2.

$$7=-x^{2}-2x+2x+4$$

Combine -2x and 2x to get 0.

$$7=-x^{2}+4$$

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

$$-x^{2}+4=7$$

Subtract 4 from both sides.

$$-x^{2}=7-4$$

Subtract 4 from 7 to get 3.

$$-x^{2}=3$$

Divide both sides by -1.

$$x^{2}=-3$$

The equation is now solved.

$$x=\sqrt{3}i x=-\sqrt{3}i$$

Steps Using the Quadratic Formula

To find the opposite of x-2, find the opposite of each term.

$$7=\left(-x-\left(-2\right)\right)\left(x+2\right)$$

The opposite of -2 is 2.

$$7=\left(-x+2\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of -x+2 by each term of x+2.

$$7=-x^{2}-2x+2x+4$$

Combine -2x and 2x to get 0.

$$7=-x^{2}+4$$

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

$$-x^{2}+4=7$$

Subtract 7 from both sides.

$$-x^{2}+4-7=0$$

Subtract 7 from 4 to get -3.

$$-x^{2}-3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-3\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-3\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-3\right)}}{2\left(-1\right)}$$

Multiply 4 times -3.

$$x=\frac{0±\sqrt{-12}}{2\left(-1\right)}$$

Take the square root of -12.

$$x=\frac{0±2\sqrt{3}i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2\sqrt{3}i}{-2}$$

Now solve the equation x=\frac{0±2\sqrt{3}i}{-2} when ± is plus.

$$x=-\sqrt{3}i$$

Now solve the equation x=\frac{0±2\sqrt{3}i}{-2} when ± is minus.

$$x=\sqrt{3}i$$

The equation is now solved.

$$x=-\sqrt{3}i x=\sqrt{3}i$$