Solve 48^2+25=x^2

$$48 ^ { 2 } + 25 = x ^ { 2 }$$

Solve for x

$$x=\sqrt{2329}\approx 48.259714048$$

$$x=-\sqrt{2329}\approx -48.259714048$$

Steps by Finding Square Root

Calculate 48 to the power of 2 and get 2304.

$$2304+25=x^{2}$$

Add 2304 and 25 to get 2329.

$$2329=x^{2}$$

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

$$x^{2}=2329$$

Take the square root of both sides of the equation.

$$x=\sqrt{2329} x=-\sqrt{2329}$$

Steps Using the Quadratic Formula

Calculate 48 to the power of 2 and get 2304.

$$2304+25=x^{2}$$

Add 2304 and 25 to get 2329.

$$2329=x^{2}$$

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

$$x^{2}=2329$$

Subtract 2329 from both sides.

$$x^{2}-2329=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2329 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2329\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2329\right)}}{2}$$

Multiply -4 times -2329.

$$x=\frac{0±\sqrt{9316}}{2}$$

Take the square root of 9316.

$$x=\frac{0±2\sqrt{2329}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{2329}}{2} when ± is plus.

$$x=\sqrt{2329}$$

Now solve the equation x=\frac{0±2\sqrt{2329}}{2} when ± is minus.

$$x=-\sqrt{2329}$$

The equation is now solved.

$$x=\sqrt{2329} x=-\sqrt{2329}$$