Find All Complex Solutions 18x^2+25=475

$18 x^{2} + 25 = 475$

Step 1

Move all terms to the left side of the equation and simplify.

Subtract $475$ from both sides of the equation.

$18 x^{2} + 25 - 475 = 0$

Subtract $475$ from $25$ .

$18 x^{2} - 450 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 18$ , $b = 0$ , and $c = - 450$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (18 \cdot - 450)}}{2 \cdot 18}$

Step 4

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 18 \cdot - 450}}{2 \cdot 18}$

Multiply $- 4 \cdot 18 \cdot - 450$ .

Multiply $- 4$ by $18$ .

$x = \frac{0 \pm \sqrt{0 - 72 \cdot - 450}}{2 \cdot 18}$

Multiply $- 72$ by $- 450$ .

$x = \frac{0 \pm \sqrt{0 + 32400}}{2 \cdot 18}$

Add $0$ and $32400$ .

$x = \frac{0 \pm \sqrt{32400}}{2 \cdot 18}$

Rewrite $32400$ as $180^{2}$ .

$x = \frac{0 \pm \sqrt{180^{2}}}{2 \cdot 18}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{0 \pm 180}{2 \cdot 18}$

Multiply $2$ by $18$ .

$x = \frac{0 \pm 180}{36}$

Simplify $\frac{0 \pm 180}{36}$ .

$x = \pm 5$

Step 5

The final answer is the combination of both solutions.

$x = 5, - 5$