Solve x^2=35.5^2-5.5^2

$${ x }^{ 2 } = { 35.5 }^{ 2 } - { 5.5 }^{ 2 }$$

Solve for x

$$x=\sqrt{1230}\approx 35.071355834$$

$$x=-\sqrt{1230}\approx -35.071355834$$

Steps by Finding Square Root

Calculate 35.5 to the power of 2 and get 1260.25.

$$x^{2}=1260.25-5.5^{2}$$

Calculate 5.5 to the power of 2 and get 30.25.

$$x^{2}=1260.25-30.25$$

Subtract 30.25 from 1260.25 to get 1230.

$$x^{2}=1230$$

Take the square root of both sides of the equation.

$$x=\sqrt{1230} x=-\sqrt{1230}$$

Steps Using the Quadratic Formula

Calculate 35.5 to the power of 2 and get 1260.25.

$$x^{2}=1260.25-5.5^{2}$$

Calculate 5.5 to the power of 2 and get 30.25.

$$x^{2}=1260.25-30.25$$

Subtract 30.25 from 1260.25 to get 1230.

$$x^{2}=1230$$

Subtract 1230 from both sides.

$$x^{2}-1230=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1230 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1230\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1230\right)}}{2}$$

Multiply -4 times -1230.

$$x=\frac{0±\sqrt{4920}}{2}$$

Take the square root of 4920.

$$x=\frac{0±2\sqrt{1230}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{1230}}{2} when ± is plus.

$$x=\sqrt{1230}$$

Now solve the equation x=\frac{0±2\sqrt{1230}}{2} when ± is minus.

$$x=-\sqrt{1230}$$

The equation is now solved.

$$x=\sqrt{1230} x=-\sqrt{1230}$$