Solve (x)x+5/4=7/8

$$( x ) x + \frac { 5 } { 4 } = \frac { 7 } { 8 }$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{6}i}{4}\approx -0-0.612372436i$$

$$x=\frac{\sqrt{6}i}{4}\approx 0.612372436i$$

Steps by Finding Square Root

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

$$x^{2}+\frac{5}{4}=\frac{7}{8}$$

Subtract \frac{5}{4} from both sides.

$$x^{2}=\frac{7}{8}-\frac{5}{4}$$

Least common multiple of 8 and 4 is 8. Convert \frac{7}{8} and \frac{5}{4} to fractions with denominator 8.

$$x^{2}=\frac{7}{8}-\frac{10}{8}$$

Since \frac{7}{8} and \frac{10}{8} have the same denominator, subtract them by subtracting their numerators.

$$x^{2}=\frac{7-10}{8}$$

Subtract 10 from 7 to get -3.

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

The equation is now solved.

$$x=\frac{\sqrt{6}i}{4} x=-\frac{\sqrt{6}i}{4}$$

Steps Using the Quadratic Formula

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

$$x^{2}+\frac{5}{4}=\frac{7}{8}$$

Subtract \frac{7}{8} from both sides.

$$x^{2}+\frac{5}{4}-\frac{7}{8}=0$$

Least common multiple of 4 and 8 is 8. Convert \frac{5}{4} and \frac{7}{8} to fractions with denominator 8.

$$x^{2}+\frac{10}{8}-\frac{7}{8}=0$$

Since \frac{10}{8} and \frac{7}{8} have the same denominator, subtract them by subtracting their numerators.

$$x^{2}+\frac{10-7}{8}=0$$

Subtract 7 from 10 to get 3.

$$x^{2}+\frac{3}{8}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{3}{8} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{8}}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{3}{8}}}{2}$$

Multiply -4 times \frac{3}{8}.

$$x=\frac{0±\sqrt{-\frac{3}{2}}}{2}$$

Take the square root of -\frac{3}{2}.

$$x=\frac{0±\frac{\sqrt{6}i}{2}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{6}i}{2}}{2} when ± is plus.

$$x=\frac{\sqrt{6}i}{4}$$

Now solve the equation x=\frac{0±\frac{\sqrt{6}i}{2}}{2} when ± is minus.

$$x=-\frac{\sqrt{6}i}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{6}i}{4} x=-\frac{\sqrt{6}i}{4}$$