Solve x^2=9^2+4^5

$$x ^ { 2 } = 9 ^ { 2 } + 4 ^ { 5 }$$

Solve for x

$$x=\sqrt{1105}\approx 33.241540277$$

$$x=-\sqrt{1105}\approx -33.241540277$$

Steps by Finding Square Root

Calculate 9 to the power of 2 and get 81.

$$x^{2}=81+4^{5}$$

Calculate 4 to the power of 5 and get 1024.

$$x^{2}=81+1024$$

Add 81 and 1024 to get 1105.

$$x^{2}=1105$$

Take the square root of both sides of the equation.

$$x=\sqrt{1105} x=-\sqrt{1105}$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 2 and get 81.

$$x^{2}=81+4^{5}$$

Calculate 4 to the power of 5 and get 1024.

$$x^{2}=81+1024$$

Add 81 and 1024 to get 1105.

$$x^{2}=1105$$

Subtract 1105 from both sides.

$$x^{2}-1105=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1105 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1105\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1105\right)}}{2}$$

Multiply -4 times -1105.

$$x=\frac{0±\sqrt{4420}}{2}$$

Take the square root of 4420.

$$x=\frac{0±2\sqrt{1105}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{1105}}{2} when ± is plus.

$$x=\sqrt{1105}$$

Now solve the equation x=\frac{0±2\sqrt{1105}}{2} when ± is minus.

$$x=-\sqrt{1105}$$

The equation is now solved.

$$x=\sqrt{1105} x=-\sqrt{1105}$$