Solve x^2=2500*3+150^2

$$x ^ { 2 } = 2500 \cdot 3 + 150 ^ { 2 }$$

Solve for x

$$x=100\sqrt{3}\approx 173.205080757$$

$$x=-100\sqrt{3}\approx -173.205080757$$

Steps by Finding Square Root

Multiply 2500 and 3 to get 7500.

$$x^{2}=7500+150^{2}$$

Calculate 150 to the power of 2 and get 22500.

$$x^{2}=7500+22500$$

Add 7500 and 22500 to get 30000.

$$x^{2}=30000$$

Take the square root of both sides of the equation.

$$x=100\sqrt{3} x=-100\sqrt{3}$$

Steps Using the Quadratic Formula

Multiply 2500 and 3 to get 7500.

$$x^{2}=7500+150^{2}$$

Calculate 150 to the power of 2 and get 22500.

$$x^{2}=7500+22500$$

Add 7500 and 22500 to get 30000.

$$x^{2}=30000$$

Subtract 30000 from both sides.

$$x^{2}-30000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -30000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-30000\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-30000\right)}}{2}$$

Multiply -4 times -30000.

$$x=\frac{0±\sqrt{120000}}{2}$$

Take the square root of 120000.

$$x=\frac{0±200\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±200\sqrt{3}}{2} when ± is plus.

$$x=100\sqrt{3}$$

Now solve the equation x=\frac{0±200\sqrt{3}}{2} when ± is minus.

$$x=-100\sqrt{3}$$

The equation is now solved.

$$x=100\sqrt{3} x=-100\sqrt{3}$$