Question

Solve for x:

5x^2 + 4x - 1 = 0

a) x = 1, x = 5
b) x = -1, x = -5
c) x = -1, x = 1/5
d) x = -1/5, x = -5

Answer 1

The quadratic equation 5x^2 + 4x - 1 = 0 can be solved using the quadratic formula, yielding two solutions: x = 0.2 and x = -1.

Step-by-step explanation:

The quadratic equation in question is 5x^2 + 4x - 1 = 0. This equation can be solved by using the quadratic formula, which is expressed as x = [-b ± √(b^2 - 4ac)]/(2a) where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0. In this case, a = 5, b = 4, and c = -1. Substituting these values into the quadratic formula, we have:

x = [-(4) ± √((4)^2 - 4(5)(-1))]/(2(5))
= [-4 ± √(16 + 20)]/10
= [-4 ± √(36)]/10
= [-4 ± 6]/10

Hence, there are two possible solutions for x:

x = (-4 + 6)/10 = 2/10 = 0.2
x = (-4 - 6)/10 = -10/10 = -1

Therefore, the solutions for the equation are x = 0.2 and x = -1.