Question

Find the values of x that satisfy the equation

5+2(5x+2x^2)=13
Give each value in its simplest surd form

Answer 1

Step-by-step explanation:

Answer 2

To find the values of x that satisfy the equation 5 + 2(5x + 2x^2) = 13, we can simplify the equation and solve it using the quadratic formula. The solutions are x = (-10 ± sqrt(228)) / 8.

Step-by-step explanation:

To find the values of x that satisfy the equation 5 + 2(5x + 2x^2) = 13, we can start by simplifying the equation:

5 + 10x + 4x^2 = 13

4x^2 + 10x - 8 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

For our equation, a = 4, b = 10, and c = -8:

x = (-10 ± sqrt(10^2 - 4 * 4 * -8)) / (2 * 4)

x = (-10 ± sqrt(100 + 128)) / 8

x = (-10 ± sqrt(228)) / 8

Since the square root of 228 is not a simple surd, we can leave the solution as x = (-10 ± sqrt(228)) / 8.