Solve +6^2=-k/4+sqrt{21/16+6}

$$+ 6 ^ { 2 } = - \frac { k } { 4 } + \sqrt { \frac { 21 } { 16 } + 6 }$$

Solve for k

$$k=3\left(\sqrt{13}-48\right)\approx -133.183346174$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$4\times 6^{2}=-k+4\sqrt{\frac{21}{16}+6}$$

Calculate 6 to the power of 2 and get 36.

$$4\times 36=-k+4\sqrt{\frac{21}{16}+6}$$

Multiply 4 and 36 to get 144.

$$144=-k+4\sqrt{\frac{21}{16}+6}$$

Convert 6 to fraction \frac{96}{16}.

$$144=-k+4\sqrt{\frac{21}{16}+\frac{96}{16}}$$

Since \frac{21}{16} and \frac{96}{16} have the same denominator, add them by adding their numerators.

$$144=-k+4\sqrt{\frac{21+96}{16}}$$

Add 21 and 96 to get 117.

$$144=-k+4\sqrt{\frac{117}{16}}$$

Rewrite the square root of the division \sqrt{\frac{117}{16}} as the division of square roots \frac{\sqrt{117}}{\sqrt{16}}.

$$144=-k+4\times \frac{\sqrt{117}}{\sqrt{16}}$$

Factor 117=3^{2}\times 13. Rewrite the square root of the product \sqrt{3^{2}\times 13} as the product of square roots \sqrt{3^{2}}\sqrt{13}. Take the square root of 3^{2}.

$$144=-k+4\times \frac{3\sqrt{13}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$144=-k+4\times \frac{3\sqrt{13}}{4}$$

Express 4\times \frac{3\sqrt{13}}{4} as a single fraction.

$$144=-k+\frac{4\times 3\sqrt{13}}{4}$$

Cancel out 4 and 4.

$$144=-k+3\sqrt{13}$$

Swap sides so that all variable terms are on the left hand side.

$$-k+3\sqrt{13}=144$$

Subtract 3\sqrt{13} from both sides.

$$-k=144-3\sqrt{13}$$

Divide both sides by -1.

$$\frac{-k}{-1}=\frac{144-3\sqrt{13}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$k=\frac{144-3\sqrt{13}}{-1}$$

Divide 144-3\sqrt{13} by -1.

$$k=3\sqrt{13}-144$$