Solve x=-5/8-sqrt{{left(-5/8right)}^2+6/4}

$$x=- \frac{ 5 }{ 8 } - \sqrt{ { \left(- \frac{ 5 }{ 8 } \right) }^{ 2 } + \frac{ 6 }{ 4 } }$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Calculate -\frac{5}{8} to the power of 2 and get \frac{25}{64}.

$$x=-\frac{5}{8}-\sqrt{\frac{25}{64}+\frac{6}{4}}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$x=-\frac{5}{8}-\sqrt{\frac{25}{64}+\frac{3}{2}}$$

Least common multiple of 64 and 2 is 64. Convert \frac{25}{64} and \frac{3}{2} to fractions with denominator 64.

$$x=-\frac{5}{8}-\sqrt{\frac{25}{64}+\frac{96}{64}}$$

Since \frac{25}{64} and \frac{96}{64} have the same denominator, add them by adding their numerators.

$$x=-\frac{5}{8}-\sqrt{\frac{25+96}{64}}$$

Add 25 and 96 to get 121.

$$x=-\frac{5}{8}-\sqrt{\frac{121}{64}}$$

Rewrite the square root of the division \frac{121}{64} as the division of square roots \frac{\sqrt{121}}{\sqrt{64}}. Take the square root of both numerator and denominator.

$$x=-\frac{5}{8}-\frac{11}{8}$$

Since -\frac{5}{8} and \frac{11}{8} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{-5-11}{8}$$

Subtract 11 from -5 to get -16.

$$x=\frac{-16}{8}$$

Divide -16 by 8 to get -2.

$$x=-2$$

Assign x

$$x≔-2$$