Solve 4x(x+8)=6(x+8)

$$4x(x+8)=6(x+8)$$

Solve for x

$$x=-8$$

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps Using the Quadratic Formula

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

$$4x^{2}+32x=6\left(x+8\right)$$

Use the distributive property to multiply 6 by x+8.

$$4x^{2}+32x=6x+48$$

Subtract 6x from both sides.

$$4x^{2}+32x-6x=48$$

Combine 32x and -6x to get 26x.

$$4x^{2}+26x=48$$

Subtract 48 from both sides.

$$4x^{2}+26x-48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 26 for b, and -48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-26±\sqrt{26^{2}-4\times 4\left(-48\right)}}{2\times 4}$$

Square 26.

$$x=\frac{-26±\sqrt{676-4\times 4\left(-48\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-26±\sqrt{676-16\left(-48\right)}}{2\times 4}$$

Multiply -16 times -48.

$$x=\frac{-26±\sqrt{676+768}}{2\times 4}$$

Add 676 to 768.

$$x=\frac{-26±\sqrt{1444}}{2\times 4}$$

Take the square root of 1444.

$$x=\frac{-26±38}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{-26±38}{8}$$

Now solve the equation x=\frac{-26±38}{8} when ± is plus. Add -26 to 38.

$$x=\frac{12}{8}$$

Reduce the fraction \frac{12}{8} to lowest terms by extracting and canceling out 4.

$$x=\frac{3}{2}$$

Now solve the equation x=\frac{-26±38}{8} when ± is minus. Subtract 38 from -26.

$$x=-\frac{64}{8}$$

Divide -64 by 8.

$$x=-8$$

The equation is now solved.

$$x=\frac{3}{2} x=-8$$

Steps for Completing the Square

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

$$4x^{2}+32x=6\left(x+8\right)$$

Use the distributive property to multiply 6 by x+8.

$$4x^{2}+32x=6x+48$$

Subtract 6x from both sides.

$$4x^{2}+32x-6x=48$$

Combine 32x and -6x to get 26x.

$$4x^{2}+26x=48$$

Divide both sides by 4.

$$\frac{4x^{2}+26x}{4}=\frac{48}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\frac{26}{4}x=\frac{48}{4}$$

Reduce the fraction \frac{26}{4} to lowest terms by extracting and canceling out 2.

$$x^{2}+\frac{13}{2}x=\frac{48}{4}$$

Divide 48 by 4.

$$x^{2}+\frac{13}{2}x=12$$

Divide \frac{13}{2}, the coefficient of the x term, by 2 to get \frac{13}{4}. Then add the square of \frac{13}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{13}{2}x+\left(\frac{13}{4}\right)^{2}=12+\left(\frac{13}{4}\right)^{2}$$

Square \frac{13}{4} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{13}{2}x+\frac{169}{16}=12+\frac{169}{16}$$

Add 12 to \frac{169}{16}.

$$x^{2}+\frac{13}{2}x+\frac{169}{16}=\frac{361}{16}$$

Factor x^{2}+\frac{13}{2}x+\frac{169}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{13}{4}\right)^{2}=\frac{361}{16}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{13}{4}\right)^{2}}=\sqrt{\frac{361}{16}}$$

Simplify.

$$x+\frac{13}{4}=\frac{19}{4} x+\frac{13}{4}=-\frac{19}{4}$$

Subtract \frac{13}{4} from both sides of the equation.

$$x=\frac{3}{2} x=-8$$