Solve {left(45/7right)}^2+25=x^2

$${ \left( \frac{ 45 }{ 7 } \right) }^{ 2 } +25= { x }^{ 2 }$$

Solve for x

$$x = \frac{5 \sqrt{130}}{7} \approx 8.144110179$$

$$x = -\frac{5 \sqrt{130}}{7} \approx -8.144110179$$

Steps by Finding Square Root

Calculate \frac{45}{7} to the power of 2 and get \frac{2025}{49}.

$$\frac{2025}{49}+25=x^{2}$$

Add \frac{2025}{49} and 25 to get \frac{3250}{49}.

$$\frac{3250}{49}=x^{2}$$

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

$$x^{2}=\frac{3250}{49}$$

Take the square root of both sides of the equation.

$$x=\frac{5\sqrt{130}}{7} x=-\frac{5\sqrt{130}}{7}$$

Steps Using the Quadratic Formula

Calculate \frac{45}{7} to the power of 2 and get \frac{2025}{49}.

$$\frac{2025}{49}+25=x^{2}$$

Add \frac{2025}{49} and 25 to get \frac{3250}{49}.

$$\frac{3250}{49}=x^{2}$$

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

$$x^{2}=\frac{3250}{49}$$

Subtract \frac{3250}{49} from both sides.

$$x^{2}-\frac{3250}{49}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{3250}{49} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{3250}{49}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{3250}{49}\right)}}{2}$$

Multiply -4 times -\frac{3250}{49}.

$$x=\frac{0±\sqrt{\frac{13000}{49}}}{2}$$

Take the square root of \frac{13000}{49}.

$$x=\frac{0±\frac{10\sqrt{130}}{7}}{2}$$

Now solve the equation x=\frac{0±\frac{10\sqrt{130}}{7}}{2} when ± is plus.

$$x=\frac{5\sqrt{130}}{7}$$

Now solve the equation x=\frac{0±\frac{10\sqrt{130}}{7}}{2} when ± is minus.

$$x=-\frac{5\sqrt{130}}{7}$$

The equation is now solved.

$$x=\frac{5\sqrt{130}}{7} x=-\frac{5\sqrt{130}}{7}$$