Solve Using the Quadratic Formula x^2+45x=-200

$x^{2} + 45 x = - 200$

Step 1

Add $200$ to both sides of the equation.

$x^{2} + 45 x + 200 = 0$

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 $a = 1$ , $b = 45$ , and $c = 200$ into the quadratic formula and solve for $x$ .

$\frac{- 45 \pm \sqrt{45^{2} - 4 \cdot (1 \cdot 200)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $45$ to the power of $2$ .

$x = \frac{- 45 \pm \sqrt{2025 - 4 \cdot 1 \cdot 200}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 200$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 45 \pm \sqrt{2025 - 4 \cdot 200}}{2 \cdot 1}$

Multiply $- 4$ by $200$ .

$x = \frac{- 45 \pm \sqrt{2025 - 800}}{2 \cdot 1}$

Subtract $800$ from $2025$ .

$x = \frac{- 45 \pm \sqrt{1225}}{2 \cdot 1}$

Rewrite $1225$ as $35^{2}$ .

$x = \frac{- 45 \pm \sqrt{35^{2}}}{2 \cdot 1}$

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

$x = \frac{- 45 \pm 35}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 45 \pm 35}{2}$

Step 5

The final answer is the combination of both solutions.

$x = - 5, - 40$