Solve 7^2+x^2=14^2

$${ 7 }^{ 2 } + { x }^{ 2 } = { 14 }^{ 2 }$$

Solve for x

$$x=7\sqrt{3}\approx 12.124355653$$

$$x=-7\sqrt{3}\approx -12.124355653$$

Steps by Finding Square Root

Calculate 7 to the power of 2 and get 49.

$$49+x^{2}=14^{2}$$

Calculate 14 to the power of 2 and get 196.

$$49+x^{2}=196$$

Subtract 49 from both sides.

$$x^{2}=196-49$$

Subtract 49 from 196 to get 147.

$$x^{2}=147$$

Take the square root of both sides of the equation.

$$x=7\sqrt{3} x=-7\sqrt{3}$$

Steps Using the Quadratic Formula

Calculate 7 to the power of 2 and get 49.

$$49+x^{2}=14^{2}$$

Calculate 14 to the power of 2 and get 196.

$$49+x^{2}=196$$

Subtract 196 from both sides.

$$49+x^{2}-196=0$$

Subtract 196 from 49 to get -147.

$$-147+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-147=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -147 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-147\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-147\right)}}{2}$$

Multiply -4 times -147.

$$x=\frac{0±\sqrt{588}}{2}$$

Take the square root of 588.

$$x=\frac{0±14\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±14\sqrt{3}}{2} when ± is plus.

$$x=7\sqrt{3}$$

Now solve the equation x=\frac{0±14\sqrt{3}}{2} when ± is minus.

$$x=-7\sqrt{3}$$

The equation is now solved.

$$x=7\sqrt{3} x=-7\sqrt{3}$$