Solve 4s(s+3)=s-6

$$4 s ( s + 3 ) = s - 6$$

Solve for s

$$s=-\frac{3}{4}=-0.75$$

$$s=-2$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 4s by s+3.

$$4s^{2}+12s=s-6$$

Subtract s from both sides.

$$4s^{2}+12s-s=-6$$

Combine 12s and -s to get 11s.

$$4s^{2}+11s=-6$$

Add 6 to both sides.

$$4s^{2}+11s+6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 11 for b, and 6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{-11±\sqrt{11^{2}-4\times 4\times 6}}{2\times 4}$$

Square 11.

$$s=\frac{-11±\sqrt{121-4\times 4\times 6}}{2\times 4}$$

Multiply -4 times 4.

$$s=\frac{-11±\sqrt{121-16\times 6}}{2\times 4}$$

Multiply -16 times 6.

$$s=\frac{-11±\sqrt{121-96}}{2\times 4}$$

Add 121 to -96.

$$s=\frac{-11±\sqrt{25}}{2\times 4}$$

Take the square root of 25.

$$s=\frac{-11±5}{2\times 4}$$

Multiply 2 times 4.

$$s=\frac{-11±5}{8}$$

Now solve the equation s=\frac{-11±5}{8} when ± is plus. Add -11 to 5.

$$s=-\frac{6}{8}$$

Reduce the fraction \frac{-6}{8} to lowest terms by extracting and canceling out 2.

$$s=-\frac{3}{4}$$

Now solve the equation s=\frac{-11±5}{8} when ± is minus. Subtract 5 from -11.

$$s=-\frac{16}{8}$$

Divide -16 by 8.

$$s=-2$$

The equation is now solved.

$$s=-\frac{3}{4} s=-2$$

Steps for Completing the Square

Use the distributive property to multiply 4s by s+3.

$$4s^{2}+12s=s-6$$

Subtract s from both sides.

$$4s^{2}+12s-s=-6$$

Combine 12s and -s to get 11s.

$$4s^{2}+11s=-6$$

Divide both sides by 4.

$$\frac{4s^{2}+11s}{4}=-\frac{6}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$s^{2}+\frac{11}{4}s=-\frac{6}{4}$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

$$s^{2}+\frac{11}{4}s=-\frac{3}{2}$$

Divide \frac{11}{4}, the coefficient of the x term, by 2 to get \frac{11}{8}. Then add the square of \frac{11}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$s^{2}+\frac{11}{4}s+\left(\frac{11}{8}\right)^{2}=-\frac{3}{2}+\left(\frac{11}{8}\right)^{2}$$

Square \frac{11}{8} by squaring both the numerator and the denominator of the fraction.

$$s^{2}+\frac{11}{4}s+\frac{121}{64}=-\frac{3}{2}+\frac{121}{64}$$

Add -\frac{3}{2} to \frac{121}{64} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$s^{2}+\frac{11}{4}s+\frac{121}{64}=\frac{25}{64}$$

Factor s^{2}+\frac{11}{4}s+\frac{121}{64}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(s+\frac{11}{8}\right)^{2}=\frac{25}{64}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(s+\frac{11}{8}\right)^{2}}=\sqrt{\frac{25}{64}}$$

Simplify.

$$s+\frac{11}{8}=\frac{5}{8} s+\frac{11}{8}=-\frac{5}{8}$$

Subtract \frac{11}{8} from both sides of the equation.

$$s=-\frac{3}{4} s=-2$$