Solve 4.5^2+x^2=9^2

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

Solve for x

$$x = \frac{9 \sqrt{3}}{2} \approx 7.794228634$$

$$x = -\frac{9 \sqrt{3}}{2} \approx -7.794228634$$

Steps by Finding Square Root

Calculate 4.5 to the power of 2 and get 20.25.

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

Calculate 9 to the power of 2 and get 81.

$$20.25+x^{2}=81$$

Subtract 20.25 from both sides.

$$x^{2}=81-20.25$$

Subtract 20.25 from 81 to get 60.75.

$$x^{2}=60.75$$

Take the square root of both sides of the equation.

$$x=\frac{9\sqrt{3}}{2} x=-\frac{9\sqrt{3}}{2}$$

Steps Using the Quadratic Formula

Calculate 4.5 to the power of 2 and get 20.25.

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

Calculate 9 to the power of 2 and get 81.

$$20.25+x^{2}=81$$

Subtract 81 from both sides.

$$20.25+x^{2}-81=0$$

Subtract 81 from 20.25 to get -60.75.

$$-60.75+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-60.75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -60.75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-60.75\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-60.75\right)}}{2}$$

Multiply -4 times -60.75.

$$x=\frac{0±\sqrt{243}}{2}$$

Take the square root of 243.

$$x=\frac{0±9\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±9\sqrt{3}}{2} when ± is plus.

$$x=\frac{9\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±9\sqrt{3}}{2} when ± is minus.

$$x=-\frac{9\sqrt{3}}{2}$$

The equation is now solved.

$$x=\frac{9\sqrt{3}}{2} x=-\frac{9\sqrt{3}}{2}$$