Solve x^2+3^2=73^8

$$x ^ { 2 } + 3 ^ { 2 } = 73 ^ { 8 }$$

Solve for x

$$x=14\sqrt{4114592305582}\approx 28398240.999999844$$

$$x=-14\sqrt{4114592305582}\approx -28398240.999999844$$

Steps by Finding Square Root

Calculate 3 to the power of 2 and get 9.

$$x^{2}+9=73^{8}$$

Calculate 73 to the power of 8 and get 806460091894081.

$$x^{2}+9=806460091894081$$

Subtract 9 from both sides.

$$x^{2}=806460091894081-9$$

Subtract 9 from 806460091894081 to get 806460091894072.

$$x^{2}=806460091894072$$

Take the square root of both sides of the equation.

$$x=14\sqrt{4114592305582} x=-14\sqrt{4114592305582}$$

Steps Using the Quadratic Formula

Calculate 3 to the power of 2 and get 9.

$$x^{2}+9=73^{8}$$

Calculate 73 to the power of 8 and get 806460091894081.

$$x^{2}+9=806460091894081$$

Subtract 806460091894081 from both sides.

$$x^{2}+9-806460091894081=0$$

Subtract 806460091894081 from 9 to get -806460091894072.

$$x^{2}-806460091894072=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -806460091894072 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-806460091894072\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-806460091894072\right)}}{2}$$

Multiply -4 times -806460091894072.

$$x=\frac{0±\sqrt{3225840367576288}}{2}$$

Take the square root of 3225840367576288.

$$x=\frac{0±28\sqrt{4114592305582}}{2}$$

Now solve the equation x=\frac{0±28\sqrt{4114592305582}}{2} when ± is plus.

$$x=14\sqrt{4114592305582}$$

Now solve the equation x=\frac{0±28\sqrt{4114592305582}}{2} when ± is minus.

$$x=-14\sqrt{4114592305582}$$

The equation is now solved.

$$x=14\sqrt{4114592305582} x=-14\sqrt{4114592305582}$$