Question

Y=.5x+4 Y= -.25x^2+5 Using the quadratic formula, what are the solutions?

Answer 1

Hi there!

$\large\boxed{x = -1 \pm \sqrt{5}}$

We can solve by setting both equations equal to each other:

.5x + 4 = -.25x² + 5

Move everything to one side:

0 = -.25x² - .5x + 1

Multiply both sides by 4 to cancel out the decimals:

0 = -x² - 2x + 4

Factor out negative from both sides:

0 = x² + 2x - 4

Use the quadratic formula:

$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

Plug in the corresponding terms:

$x = \frac{-2 \pm \sqrt{4-4(-4)(1)}}{2}$

Simplify:

$x = \frac{-2 \pm \sqrt{4 + 16}}{2}\\\\x = \frac{-2 \pm \sqrt{20}}{2}$

Simplify the radical to reduce:

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

Divide all terms by 2:

$x = -1 \pm \sqrt{5}$