Solve 2x(x+6)-4(x+6)=-(x+6)div2

$$2x(x+6)-4(x+6)=-(x+6) \div 2$$

Solve for x

$$x=-6$$

$$x = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$4x\left(x+6\right)-8\left(x+6\right)=-\left(x+6\right)$$

Use the distributive property to multiply 4x by x+6.

$$4x^{2}+24x-8\left(x+6\right)=-\left(x+6\right)$$

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

$$4x^{2}+24x-8x-48=-\left(x+6\right)$$

Combine 24x and -8x to get 16x.

$$4x^{2}+16x-48=-\left(x+6\right)$$

To find the opposite of x+6, find the opposite of each term.

$$4x^{2}+16x-48=-x-6$$

Add x to both sides.

$$4x^{2}+16x-48+x=-6$$

Combine 16x and x to get 17x.

$$4x^{2}+17x-48=-6$$

Add 6 to both sides.

$$4x^{2}+17x-48+6=0$$

Add -48 and 6 to get -42.

$$4x^{2}+17x-42=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 17 for b, and -42 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-17±\sqrt{17^{2}-4\times 4\left(-42\right)}}{2\times 4}$$

Square 17.

$$x=\frac{-17±\sqrt{289-4\times 4\left(-42\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-17±\sqrt{289-16\left(-42\right)}}{2\times 4}$$

Multiply -16 times -42.

$$x=\frac{-17±\sqrt{289+672}}{2\times 4}$$

Add 289 to 672.

$$x=\frac{-17±\sqrt{961}}{2\times 4}$$

Take the square root of 961.

$$x=\frac{-17±31}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{-17±31}{8}$$

Now solve the equation x=\frac{-17±31}{8} when ± is plus. Add -17 to 31.

$$x=\frac{14}{8}$$

Reduce the fraction \frac{14}{8} to lowest terms by extracting and canceling out 2.

$$x=\frac{7}{4}$$

Now solve the equation x=\frac{-17±31}{8} when ± is minus. Subtract 31 from -17.

$$x=-\frac{48}{8}$$

Divide -48 by 8.

$$x=-6$$

The equation is now solved.

$$x=\frac{7}{4} x=-6$$

Steps for Completing the Square

Multiply both sides of the equation by 2.

$$4x\left(x+6\right)-8\left(x+6\right)=-\left(x+6\right)$$

Use the distributive property to multiply 4x by x+6.

$$4x^{2}+24x-8\left(x+6\right)=-\left(x+6\right)$$

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

$$4x^{2}+24x-8x-48=-\left(x+6\right)$$

Combine 24x and -8x to get 16x.

$$4x^{2}+16x-48=-\left(x+6\right)$$

To find the opposite of x+6, find the opposite of each term.

$$4x^{2}+16x-48=-x-6$$

Add x to both sides.

$$4x^{2}+16x-48+x=-6$$

Combine 16x and x to get 17x.

$$4x^{2}+17x-48=-6$$

Add 48 to both sides.

$$4x^{2}+17x=-6+48$$

Add -6 and 48 to get 42.

$$4x^{2}+17x=42$$

Divide both sides by 4.

$$\frac{4x^{2}+17x}{4}=\frac{42}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\frac{17}{4}x=\frac{42}{4}$$

Reduce the fraction \frac{42}{4} to lowest terms by extracting and canceling out 2.

$$x^{2}+\frac{17}{4}x=\frac{21}{2}$$

Divide \frac{17}{4}, the coefficient of the x term, by 2 to get \frac{17}{8}. Then add the square of \frac{17}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{17}{4}x+\left(\frac{17}{8}\right)^{2}=\frac{21}{2}+\left(\frac{17}{8}\right)^{2}$$

Square \frac{17}{8} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{17}{4}x+\frac{289}{64}=\frac{21}{2}+\frac{289}{64}$$

Add \frac{21}{2} to \frac{289}{64} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{17}{4}x+\frac{289}{64}=\frac{961}{64}$$

Factor x^{2}+\frac{17}{4}x+\frac{289}{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}.

$$\left(x+\frac{17}{8}\right)^{2}=\frac{961}{64}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{17}{8}\right)^{2}}=\sqrt{\frac{961}{64}}$$

Simplify.

$$x+\frac{17}{8}=\frac{31}{8} x+\frac{17}{8}=-\frac{31}{8}$$

Subtract \frac{17}{8} from both sides of the equation.

$$x=\frac{7}{4} x=-6$$