Hi there!
[tex]\large\boxed{x = -1 \pm \sqrt{5}}[/tex]
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:
[tex]\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
Plug in the corresponding terms:
[tex]x = \frac{-2 \pm \sqrt{4-4(-4)(1)}}{2}[/tex]
Simplify:
[tex]x = \frac{-2 \pm \sqrt{4 + 16}}{2}\\\\x = \frac{-2 \pm \sqrt{20}}{2}[/tex]
Simplify the radical to reduce:
[tex]x = \frac{-2 \pm 2\sqrt{5}}{2}[/tex]
Divide all terms by 2:
[tex]x = -1 \pm \sqrt{5}[/tex]
