Solve x^2+3^2=4.5^2

$${ x }^{ 2 } + { 3 }^{ 2 } = { 4.5 }^{ 2 }$$

Solve for x

$$x = \frac{3 \sqrt{5}}{2} \approx 3.354101966$$

$$x = -\frac{3 \sqrt{5}}{2} \approx -3.354101966$$

Steps by Finding Square Root

Calculate 3 to the power of 2 and get 9.

$$x^{2}+9=4.5^{2}$$

Calculate 4.5 to the power of 2 and get 20.25.

$$x^{2}+9=20.25$$

Subtract 9 from both sides.

$$x^{2}=20.25-9$$

Subtract 9 from 20.25 to get 11.25.

$$x^{2}=11.25$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{5}}{2} x=-\frac{3\sqrt{5}}{2}$$

Steps Using the Quadratic Formula

Calculate 3 to the power of 2 and get 9.

$$x^{2}+9=4.5^{2}$$

Calculate 4.5 to the power of 2 and get 20.25.

$$x^{2}+9=20.25$$

Subtract 20.25 from both sides.

$$x^{2}+9-20.25=0$$

Subtract 20.25 from 9 to get -11.25.

$$x^{2}-11.25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -11.25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-11.25\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-11.25\right)}}{2}$$

Multiply -4 times -11.25.

$$x=\frac{0±\sqrt{45}}{2}$$

Take the square root of 45.

$$x=\frac{0±3\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±3\sqrt{5}}{2} when ± is plus.

$$x=\frac{3\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±3\sqrt{5}}{2} when ± is minus.

$$x=-\frac{3\sqrt{5}}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{5}}{2} x=-\frac{3\sqrt{5}}{2}$$