Solve (x+4)(x-1)=50

$$( x + 4 ) ( x - 1 ) = 50$$

Solve for x

$$x=-9$$

$$x=6$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+4 by x-1 and combine like terms.

$$x^{2}+3x-4=50$$

Subtract 50 from both sides.

$$x^{2}+3x-4-50=0$$

Subtract 50 from -4 to get -54.

$$x^{2}+3x-54=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 3 for b, and -54 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}-4\left(-54\right)}}{2}$$

Square 3.

$$x=\frac{-3±\sqrt{9-4\left(-54\right)}}{2}$$

Multiply -4 times -54.

$$x=\frac{-3±\sqrt{9+216}}{2}$$

Add 9 to 216.

$$x=\frac{-3±\sqrt{225}}{2}$$

Take the square root of 225.

$$x=\frac{-3±15}{2}$$

Now solve the equation x=\frac{-3±15}{2} when ± is plus. Add -3 to 15.

$$x=\frac{12}{2}$$

Divide 12 by 2.

$$x=6$$

Now solve the equation x=\frac{-3±15}{2} when ± is minus. Subtract 15 from -3.

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

Divide -18 by 2.

$$x=-9$$

The equation is now solved.

$$x=6 x=-9$$

Steps for Completing the Square

Use the distributive property to multiply x+4 by x-1 and combine like terms.

$$x^{2}+3x-4=50$$

Add 4 to both sides.

$$x^{2}+3x=50+4$$

Add 50 and 4 to get 54.

$$x^{2}+3x=54$$

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

$$x^{2}+3x+\left(\frac{3}{2}\right)^{2}=54+\left(\frac{3}{2}\right)^{2}$$

Square \frac{3}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+3x+\frac{9}{4}=54+\frac{9}{4}$$

Add 54 to \frac{9}{4}.

$$x^{2}+3x+\frac{9}{4}=\frac{225}{4}$$

Factor x^{2}+3x+\frac{9}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{3}{2}\right)^{2}=\frac{225}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{225}{4}}$$

Simplify.

$$x+\frac{3}{2}=\frac{15}{2} x+\frac{3}{2}=-\frac{15}{2}$$

Subtract \frac{3}{2} from both sides of the equation.

$$x=6 x=-9$$