Solve x^2+7^3=11

$$x ^ { 2 } + 7 ^ { 3 } = 11$$

Solve for x (complex solution)

$$x=-2\sqrt{83}i\approx -0-18.220867158i$$

$$x=2\sqrt{83}i\approx 18.220867158i$$

Steps by Finding Square Root

Calculate 7 to the power of 3 and get 343.

$$x^{2}+343=11$$

Subtract 343 from both sides.

$$x^{2}=11-343$$

Subtract 343 from 11 to get -332.

$$x^{2}=-332$$

The equation is now solved.

$$x=2\sqrt{83}i x=-2\sqrt{83}i$$

Steps Using the Quadratic Formula

Calculate 7 to the power of 3 and get 343.

$$x^{2}+343=11$$

Subtract 11 from both sides.

$$x^{2}+343-11=0$$

Subtract 11 from 343 to get 332.

$$x^{2}+332=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 332 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 332}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 332}}{2}$$

Multiply -4 times 332.

$$x=\frac{0±\sqrt{-1328}}{2}$$

Take the square root of -1328.

$$x=\frac{0±4\sqrt{83}i}{2}$$

Now solve the equation x=\frac{0±4\sqrt{83}i}{2} when ± is plus.

$$x=2\sqrt{83}i$$

Now solve the equation x=\frac{0±4\sqrt{83}i}{2} when ± is minus.

$$x=-2\sqrt{83}i$$

The equation is now solved.

$$x=2\sqrt{83}i x=-2\sqrt{83}i$$