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 √(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:

`(-b \pm √(b^2-4ac))/(2a)`

Plug in the corresponding terms:

`x = (-2 \pm √(4-4(-4)(1)))/(2)`

Simplify:

`x = (-2 \pm √(4 + 16))/(2)\\\\x = (-2 \pm √(20))/(2)`

Simplify the radical to reduce:

`x = (-2 \pm 2√(5))/(2)`

Divide all terms by 2:

`x = -1 \pm √(5)`