Solve 45=90/4+x^2

$$45 = \frac { 90 } { 4 } + x ^ { 2 }$$

Solve for x

$$x = \frac{3 \sqrt{10}}{2} \approx 4.74341649$$

$$x = -\frac{3 \sqrt{10}}{2} \approx -4.74341649$$

Steps by Finding Square Root

Reduce the fraction \frac{90}{4} to lowest terms by extracting and canceling out 2.

$$45=\frac{45}{2}+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{45}{2}+x^{2}=45$$

Subtract \frac{45}{2} from both sides.

$$x^{2}=45-\frac{45}{2}$$

Subtract \frac{45}{2} from 45 to get \frac{45}{2}.

$$x^{2}=\frac{45}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{10}}{2} x=-\frac{3\sqrt{10}}{2}$$

Steps Using the Quadratic Formula

Reduce the fraction \frac{90}{4} to lowest terms by extracting and canceling out 2.

$$45=\frac{45}{2}+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{45}{2}+x^{2}=45$$

Subtract 45 from both sides.

$$\frac{45}{2}+x^{2}-45=0$$

Subtract 45 from \frac{45}{2} to get -\frac{45}{2}.

$$-\frac{45}{2}+x^{2}=0$$

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.

$$x^{2}-\frac{45}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{45}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{45}{2}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{45}{2}\right)}}{2}$$

Multiply -4 times -\frac{45}{2}.

$$x=\frac{0±\sqrt{90}}{2}$$

Take the square root of 90.

$$x=\frac{0±3\sqrt{10}}{2}$$

Now solve the equation x=\frac{0±3\sqrt{10}}{2} when ± is plus.

$$x=\frac{3\sqrt{10}}{2}$$

Now solve the equation x=\frac{0±3\sqrt{10}}{2} when ± is minus.

$$x=-\frac{3\sqrt{10}}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{10}}{2} x=-\frac{3\sqrt{10}}{2}$$