Solve 64=(x^2+4^2)+(23^3+4)

$$64 = ( x ^ { 2 } + 4 ^ { 2 } ) + ( 23 ^ { 3 } + 4 )$$

Solve for x (complex solution)

$$x=-3\sqrt{1347}i\approx -0-110.104495821i$$

$$x=3\sqrt{1347}i\approx 110.104495821i$$

Steps by Finding Square Root

Calculate 4 to the power of 2 and get 16.

$$64=x^{2}+16+23^{3}+4$$

Calculate 23 to the power of 3 and get 12167.

$$64=x^{2}+16+12167+4$$

Add 16 and 12167 to get 12183.

$$64=x^{2}+12183+4$$

Add 12183 and 4 to get 12187.

$$64=x^{2}+12187$$

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

$$x^{2}+12187=64$$

Subtract 12187 from both sides.

$$x^{2}=64-12187$$

Subtract 12187 from 64 to get -12123.

$$x^{2}=-12123$$

The equation is now solved.

$$x=3\sqrt{1347}i x=-3\sqrt{1347}i$$

Steps Using the Quadratic Formula

Calculate 4 to the power of 2 and get 16.

$$64=x^{2}+16+23^{3}+4$$

Calculate 23 to the power of 3 and get 12167.

$$64=x^{2}+16+12167+4$$

Add 16 and 12167 to get 12183.

$$64=x^{2}+12183+4$$

Add 12183 and 4 to get 12187.

$$64=x^{2}+12187$$

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

$$x^{2}+12187=64$$

Subtract 64 from both sides.

$$x^{2}+12187-64=0$$

Subtract 64 from 12187 to get 12123.

$$x^{2}+12123=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 12123 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 12123}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 12123}}{2}$$

Multiply -4 times 12123.

$$x=\frac{0±\sqrt{-48492}}{2}$$

Take the square root of -48492.

$$x=\frac{0±6\sqrt{1347}i}{2}$$

Now solve the equation x=\frac{0±6\sqrt{1347}i}{2} when ± is plus.

$$x=3\sqrt{1347}i$$

Now solve the equation x=\frac{0±6\sqrt{1347}i}{2} when ± is minus.

$$x=-3\sqrt{1347}i$$

The equation is now solved.

$$x=3\sqrt{1347}i x=-3\sqrt{1347}i$$