Solve 48=(x+5)(x-3)

$$48=(x+5)(x-3)$$

Solve for x

$$x=-9$$

$$x=7$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+5 by x-3 and combine like terms.

$$48=x^{2}+2x-15$$

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

$$x^{2}+2x-15=48$$

Subtract 48 from both sides.

$$x^{2}+2x-15-48=0$$

Subtract 48 from -15 to get -63.

$$x^{2}+2x-63=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 2 for b, and -63 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-63\right)}}{2}$$

Square 2.

$$x=\frac{-2±\sqrt{4-4\left(-63\right)}}{2}$$

Multiply -4 times -63.

$$x=\frac{-2±\sqrt{4+252}}{2}$$

Add 4 to 252.

$$x=\frac{-2±\sqrt{256}}{2}$$

Take the square root of 256.

$$x=\frac{-2±16}{2}$$

Now solve the equation x=\frac{-2±16}{2} when ± is plus. Add -2 to 16.

$$x=\frac{14}{2}$$

Divide 14 by 2.

$$x=7$$

Now solve the equation x=\frac{-2±16}{2} when ± is minus. Subtract 16 from -2.

$$x=-\frac{18}{2}$$

Divide -18 by 2.

$$x=-9$$

The equation is now solved.

$$x=7 x=-9$$

Steps for Completing the Square

Use the distributive property to multiply x+5 by x-3 and combine like terms.

$$48=x^{2}+2x-15$$

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

$$x^{2}+2x-15=48$$

Add 15 to both sides.

$$x^{2}+2x=48+15$$

Add 48 and 15 to get 63.

$$x^{2}+2x=63$$

Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+2x+1^{2}=63+1^{2}$$

Square 1.

$$x^{2}+2x+1=63+1$$

Add 63 to 1.

$$x^{2}+2x+1=64$$

Factor x^{2}+2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+1\right)^{2}=64$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{64}$$

Simplify.

$$x+1=8 x+1=-8$$

Subtract 1 from both sides of the equation.

$$x=7 x=-9$$