Solve 18^2+x^2=6sqrt{13}

$${ 18 }^{ 2 } + { x }^{ 2 } =6 \sqrt{ 13 }$$

Solve for x (complex solution)

$$x=-i\sqrt{324-6\sqrt{13}}\approx -0-17.388694383i$$

$$x=i\sqrt{324-6\sqrt{13}}\approx 17.388694383i$$

Steps by Finding Square Root

Calculate 18 to the power of 2 and get 324.

$$324+x^{2}=6\sqrt{13}$$

Subtract 324 from both sides.

$$x^{2}=6\sqrt{13}-324$$

The equation is now solved.

$$x=i\sqrt{324-6\sqrt{13}} x=-i\sqrt{324-6\sqrt{13}}$$

Steps Using the Quadratic Formula

Calculate 18 to the power of 2 and get 324.

$$324+x^{2}=6\sqrt{13}$$

Subtract 6\sqrt{13} from both sides.

$$324+x^{2}-6\sqrt{13}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}+324-6\sqrt{13}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 324-6\sqrt{13} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(324-6\sqrt{13}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(324-6\sqrt{13}\right)}}{2}$$

Multiply -4 times 324-6\sqrt{13}.

$$x=\frac{0±\sqrt{24\sqrt{13}-1296}}{2}$$

Take the square root of -1296+24\sqrt{13}.

$$x=\frac{0±2i\sqrt{324-6\sqrt{13}}}{2}$$

Now solve the equation x=\frac{0±2i\sqrt{324-6\sqrt{13}}}{2} when ± is plus.

$$x=i\sqrt{324-6\sqrt{13}}$$

Now solve the equation x=\frac{0±2i\sqrt{324-6\sqrt{13}}}{2} when ± is minus.

$$x=-i\sqrt{324-6\sqrt{13}}$$

The equation is now solved.

$$x=i\sqrt{324-6\sqrt{13}} x=-i\sqrt{324-6\sqrt{13}}$$