Solve x^2=30^2+1.5^2

$${ x }^{ 2 } = { 30 }^{ 2 } + { 1.5 }^{ 2 }$$

Solve for x

$$x = \frac{3 \sqrt{401}}{2} \approx 30.037476592$$

$$x = -\frac{3 \sqrt{401}}{2} \approx -30.037476592$$

Steps by Finding Square Root

Calculate 30 to the power of 2 and get 900.

$$x^{2}=900+1.5^{2}$$

Calculate 1.5 to the power of 2 and get 2.25.

$$x^{2}=900+2.25$$

Add 900 and 2.25 to get 902.25.

$$x^{2}=902.25$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{401}}{2} x=-\frac{3\sqrt{401}}{2}$$

Steps Using the Quadratic Formula

Calculate 30 to the power of 2 and get 900.

$$x^{2}=900+1.5^{2}$$

Calculate 1.5 to the power of 2 and get 2.25.

$$x^{2}=900+2.25$$

Add 900 and 2.25 to get 902.25.

$$x^{2}=902.25$$

Subtract 902.25 from both sides.

$$x^{2}-902.25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -902.25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-902.25\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-902.25\right)}}{2}$$

Multiply -4 times -902.25.

$$x=\frac{0±\sqrt{3609}}{2}$$

Take the square root of 3609.

$$x=\frac{0±3\sqrt{401}}{2}$$

Now solve the equation x=\frac{0±3\sqrt{401}}{2} when ± is plus.

$$x=\frac{3\sqrt{401}}{2}$$

Now solve the equation x=\frac{0±3\sqrt{401}}{2} when ± is minus.

$$x=-\frac{3\sqrt{401}}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{401}}{2} x=-\frac{3\sqrt{401}}{2}$$