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

F(x) = 3ˣ + 10x and g(x) = 4x – 2, find (f-g)(x)(f-g)(x) = f(x) - g(x):(3ˣ + 10x) - (4x - 2) →→→ 3ˣ + 6x - 2. Then:(f-g)(x) = 3ˣ + 6x - 2...

Y=.5x+4 Y= -.25x^2+5 Using the quadratic formula, - id54252513386503, genyjoannerubiera

harris435942

20.06.2021

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:

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

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