Solve (1div2)*(x)*(x+4)=48

$$(1 \div 2) \times (x) \times (x+4)=48$$

Solve for x

$$x=-12$$

$$x=8$$

Steps Using the Quadratic Formula

Use the distributive property to multiply \frac{1}{2}x by x+4.

$$\frac{1}{2}xx+\frac{1}{2}x\times 4=48$$

Multiply x and x to get x^{2}.

$$\frac{1}{2}x^{2}+\frac{1}{2}x\times 4=48$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\frac{1}{2}x^{2}+\frac{4}{2}x=48$$

Divide 4 by 2 to get 2.

$$\frac{1}{2}x^{2}+2x=48$$

Subtract 48 from both sides.

$$\frac{1}{2}x^{2}+2x-48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{2} for a, 2 for b, and -48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\times \frac{1}{2}\left(-48\right)}}{2\times \frac{1}{2}}$$

Square 2.

$$x=\frac{-2±\sqrt{4-4\times \frac{1}{2}\left(-48\right)}}{2\times \frac{1}{2}}$$

Multiply -4 times \frac{1}{2}.

$$x=\frac{-2±\sqrt{4-2\left(-48\right)}}{2\times \frac{1}{2}}$$

Multiply -2 times -48.

$$x=\frac{-2±\sqrt{4+96}}{2\times \frac{1}{2}}$$

Add 4 to 96.

$$x=\frac{-2±\sqrt{100}}{2\times \frac{1}{2}}$$

Take the square root of 100.

$$x=\frac{-2±10}{2\times \frac{1}{2}}$$

Multiply 2 times \frac{1}{2}.

$$x=\frac{-2±10}{1}$$

Now solve the equation x=\frac{-2±10}{1} when ± is plus. Add -2 to 10.

$$x=\frac{8}{1}$$

Divide 8 by 1.

$$x=8$$

Now solve the equation x=\frac{-2±10}{1} when ± is minus. Subtract 10 from -2.

$$x=-\frac{12}{1}$$

Divide -12 by 1.

$$x=-12$$

The equation is now solved.

$$x=8 x=-12$$

Steps for Completing the Square

Use the distributive property to multiply \frac{1}{2}x by x+4.

$$\frac{1}{2}xx+\frac{1}{2}x\times 4=48$$

Multiply x and x to get x^{2}.

$$\frac{1}{2}x^{2}+\frac{1}{2}x\times 4=48$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\frac{1}{2}x^{2}+\frac{4}{2}x=48$$

Divide 4 by 2 to get 2.

$$\frac{1}{2}x^{2}+2x=48$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}x^{2}+2x}{\frac{1}{2}}=\frac{48}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$x^{2}+\frac{2}{\frac{1}{2}}x=\frac{48}{\frac{1}{2}}$$

Divide 2 by \frac{1}{2} by multiplying 2 by the reciprocal of \frac{1}{2}.

$$x^{2}+4x=\frac{48}{\frac{1}{2}}$$

Divide 48 by \frac{1}{2} by multiplying 48 by the reciprocal of \frac{1}{2}.

$$x^{2}+4x=96$$

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

$$x^{2}+4x+2^{2}=96+2^{2}$$

Square 2.

$$x^{2}+4x+4=96+4$$

Add 96 to 4.

$$x^{2}+4x+4=100$$

Factor x^{2}+4x+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}.

$$\left(x+2\right)^{2}=100$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{100}$$

Simplify.

$$x+2=10 x+2=-10$$

Subtract 2 from both sides of the equation.

$$x=8 x=-12$$