Solve x^2+7^2=10^2

$${ x }^{ 2 } + { 7 }^{ 2 } = { 10 }^{ 2 }$$

Solve for x

$$x=\sqrt{51}\approx 7.141428429$$

$$x=-\sqrt{51}\approx -7.141428429$$

Steps by Finding Square Root

Calculate 7 to the power of 2 and get 49.

$$x^{2}+49=10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$x^{2}+49=100$$

Subtract 49 from both sides.

$$x^{2}=100-49$$

Subtract 49 from 100 to get 51.

$$x^{2}=51$$

Take the square root of both sides of the equation.

$$x=\sqrt{51} x=-\sqrt{51}$$

Steps Using the Quadratic Formula

Calculate 7 to the power of 2 and get 49.

$$x^{2}+49=10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$x^{2}+49=100$$

Subtract 100 from both sides.

$$x^{2}+49-100=0$$

Subtract 100 from 49 to get -51.

$$x^{2}-51=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -51 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-51\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-51\right)}}{2}$$

Multiply -4 times -51.

$$x=\frac{0±\sqrt{204}}{2}$$

Take the square root of 204.

$$x=\frac{0±2\sqrt{51}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{51}}{2} when ± is plus.

$$x=\sqrt{51}$$

Now solve the equation x=\frac{0±2\sqrt{51}}{2} when ± is minus.

$$x=-\sqrt{51}$$

The equation is now solved.

$$x=\sqrt{51} x=-\sqrt{51}$$