Solve (x+3)(x-1)=8(x-4)

$$(x+3)(x-1)=8(x-4)$$

Solve for x (complex solution)

$$x=3+2\sqrt{5}i\approx 3+4.472135955i$$

$$x=-2\sqrt{5}i+3\approx 3-4.472135955i$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+3 by x-1 and combine like terms.

$$x^{2}+2x-3=8\left(x-4\right)$$

Use the distributive property to multiply 8 by x-4.

$$x^{2}+2x-3=8x-32$$

Subtract 8x from both sides.

$$x^{2}+2x-3-8x=-32$$

Combine 2x and -8x to get -6x.

$$x^{2}-6x-3=-32$$

Add 32 to both sides.

$$x^{2}-6x-3+32=0$$

Add -3 and 32 to get 29.

$$x^{2}-6x+29=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -6 for b, and 29 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 29}}{2}$$

Square -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 29}}{2}$$

Multiply -4 times 29.

$$x=\frac{-\left(-6\right)±\sqrt{36-116}}{2}$$

Add 36 to -116.

$$x=\frac{-\left(-6\right)±\sqrt{-80}}{2}$$

Take the square root of -80.

$$x=\frac{-\left(-6\right)±4\sqrt{5}i}{2}$$

The opposite of -6 is 6.

$$x=\frac{6±4\sqrt{5}i}{2}$$

Now solve the equation x=\frac{6±4\sqrt{5}i}{2} when ± is plus. Add 6 to 4i\sqrt{5}.

$$x=\frac{6+4\sqrt{5}i}{2}$$

Divide 6+4i\sqrt{5} by 2.

$$x=3+2\sqrt{5}i$$

Now solve the equation x=\frac{6±4\sqrt{5}i}{2} when ± is minus. Subtract 4i\sqrt{5} from 6.

$$x=\frac{-4\sqrt{5}i+6}{2}$$

Divide 6-4i\sqrt{5} by 2.

$$x=-2\sqrt{5}i+3$$

The equation is now solved.

$$x=3+2\sqrt{5}i x=-2\sqrt{5}i+3$$

Steps for Completing the Square

Use the distributive property to multiply x+3 by x-1 and combine like terms.

$$x^{2}+2x-3=8\left(x-4\right)$$

Use the distributive property to multiply 8 by x-4.

$$x^{2}+2x-3=8x-32$$

Subtract 8x from both sides.

$$x^{2}+2x-3-8x=-32$$

Combine 2x and -8x to get -6x.

$$x^{2}-6x-3=-32$$

Add 3 to both sides.

$$x^{2}-6x=-32+3$$

Add -32 and 3 to get -29.

$$x^{2}-6x=-29$$

Divide -6, the coefficient of the x term, by 2 to get -3. Then add the square of -3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-6x+\left(-3\right)^{2}=-29+\left(-3\right)^{2}$$

Square -3.

$$x^{2}-6x+9=-29+9$$

Add -29 to 9.

$$x^{2}-6x+9=-20$$

Factor x^{2}-6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-3\right)^{2}=-20$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{-20}$$

Simplify.

$$x-3=2\sqrt{5}i x-3=-2\sqrt{5}i$$

Add 3 to both sides of the equation.

$$x=3+2\sqrt{5}i x=-2\sqrt{5}i+3$$