Question

If r(x)=4x^(2)+4x-2 and k(x)=-2x^(2)-3x+8, find all real x-values such that r(x)=k(x). x

Answer 1

To solve for x, set r(x) = k(x) and use the quadratic formula to find the solutions.

Step-by-step explanation:

We can set r(x) = k(x) and solve for x.

Given:

r(x) = 4x^(2) + 4x - 2

k(x) = -2x^(2) - 3x + 8

Set r(x) = k(x):

4x^(2) + 4x - 2 = -2x^(2) - 3x + 8

Combine like terms:

6x^(2) + 7x - 10 = 0

Now we can use the quadratic formula to find the solutions for x.

Quadratic formula: x = (-b ± sqrt(b^(2) - 4ac))/(2a)

Substitute the values from our equation:

x = (-7 ± sqrt(7^(2) - 4 * 6 * (-10)))/(2 * 6)

Simplify the expression under the square root:

x = (-7 ± sqrt(49 + 240))/(12)

x = (-7 ± sqrt(289))/(12)

Take the square root:

x = (-7 ± 17)/(12)

So, the two values of x that make r(x) = k(x) are x = 10/6 and x = -24/6.