Solve x^2+y^2-11^3-x^2=0

$$x ^ { 2 } + y ^ { 2 } - 11 ^ { 3 } - x ^ { 2 } = 0$$

Solve for y

$$y=11\sqrt{11}$$

$$y=-11\sqrt{11}$$

Steps by Finding Square Root

Calculate 11 to the power of 3 and get 1331.

$$x^{2}+y^{2}-1331-x^{2}=0$$

Combine x^{2} and -x^{2} to get 0.

$$y^{2}-1331=0$$

Add 1331 to both sides. Anything plus zero gives itself.

$$y^{2}=1331$$

Take the square root of both sides of the equation.

$$y=11\sqrt{11} y=-11\sqrt{11}$$

Steps Using the Quadratic Formula

Calculate 11 to the power of 3 and get 1331.

$$x^{2}+y^{2}-1331-x^{2}=0$$

Combine x^{2} and -x^{2} to get 0.

$$y^{2}-1331=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1331 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-1331\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-1331\right)}}{2}$$

Multiply -4 times -1331.

$$y=\frac{0±\sqrt{5324}}{2}$$

Take the square root of 5324.

$$y=\frac{0±22\sqrt{11}}{2}$$

Now solve the equation y=\frac{0±22\sqrt{11}}{2} when ± is plus.

$$y=11\sqrt{11}$$

Now solve the equation y=\frac{0±22\sqrt{11}}{2} when ± is minus.

$$y=-11\sqrt{11}$$

The equation is now solved.

$$y=11\sqrt{11} y=-11\sqrt{11}$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

$$y=11\sqrt{11}\text{ or }y=-11\sqrt{11}$$

Solve for x

$$x\in \mathrm{R}$$

$$|y|=11\sqrt{11}$$