Solve [x-(-7/8)](x-1/3)=0

$$[ x - ( - \frac { 7 } { 8 } ) ] ( x - \frac { 1 } { 3 } ) = 0$$

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

$$x=-\frac{7}{8}=-0.875$$

Steps Using the Quadratic Formula

The opposite of -\frac{7}{8} is \frac{7}{8}.

$$\left(x+\frac{7}{8}\right)\left(x-\frac{1}{3}\right)=0$$

Use the distributive property to multiply x+\frac{7}{8} by x-\frac{1}{3} and combine like terms.

$$x^{2}+\frac{13}{24}x-\frac{7}{24}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, \frac{13}{24} for b, and -\frac{7}{24} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{13}{24}±\sqrt{\left(\frac{13}{24}\right)^{2}-4\left(-\frac{7}{24}\right)}}{2}$$

Square \frac{13}{24} by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\frac{13}{24}±\sqrt{\frac{169}{576}-4\left(-\frac{7}{24}\right)}}{2}$$

Multiply -4 times -\frac{7}{24}.

$$x=\frac{-\frac{13}{24}±\sqrt{\frac{169}{576}+\frac{7}{6}}}{2}$$

Add \frac{169}{576} to \frac{7}{6} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\frac{13}{24}±\sqrt{\frac{841}{576}}}{2}$$

Take the square root of \frac{841}{576}.

$$x=\frac{-\frac{13}{24}±\frac{29}{24}}{2}$$

Now solve the equation x=\frac{-\frac{13}{24}±\frac{29}{24}}{2} when ± is plus. Add -\frac{13}{24} to \frac{29}{24} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

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

Divide \frac{2}{3} by 2.

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

Now solve the equation x=\frac{-\frac{13}{24}±\frac{29}{24}}{2} when ± is minus. Subtract \frac{29}{24} from -\frac{13}{24} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{7}{4}}{2}$$

Divide -\frac{7}{4} by 2.

$$x=-\frac{7}{8}$$

The equation is now solved.

$$x=\frac{1}{3} x=-\frac{7}{8}$$

Steps for Completing the Square

The opposite of -\frac{7}{8} is \frac{7}{8}.

$$\left(x+\frac{7}{8}\right)\left(x-\frac{1}{3}\right)=0$$

Use the distributive property to multiply x+\frac{7}{8} by x-\frac{1}{3} and combine like terms.

$$x^{2}+\frac{13}{24}x-\frac{7}{24}=0$$

Add \frac{7}{24} to both sides. Anything plus zero gives itself.

$$x^{2}+\frac{13}{24}x=\frac{7}{24}$$

Divide \frac{13}{24}, the coefficient of the x term, by 2 to get \frac{13}{48}. Then add the square of \frac{13}{48} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{13}{24}x+\left(\frac{13}{48}\right)^{2}=\frac{7}{24}+\left(\frac{13}{48}\right)^{2}$$

Square \frac{13}{48} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{13}{24}x+\frac{169}{2304}=\frac{7}{24}+\frac{169}{2304}$$

Add \frac{7}{24} to \frac{169}{2304} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{13}{24}x+\frac{169}{2304}=\frac{841}{2304}$$

Factor x^{2}+\frac{13}{24}x+\frac{169}{2304}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{13}{48}\right)^{2}=\frac{841}{2304}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{13}{48}\right)^{2}}=\sqrt{\frac{841}{2304}}$$

Simplify.

$$x+\frac{13}{48}=\frac{29}{48} x+\frac{13}{48}=-\frac{29}{48}$$

Subtract \frac{13}{48} from both sides of the equation.

$$x=\frac{1}{3} x=-\frac{7}{8}$$