What is the correct answer when you solve −5x2 + 2 + 8x = 0 using the quadratic formula?
To solve the equation −5x^2 + 2 + 8x = 0 using the quadratic formula, we need to determine the values of x that satisfy the equation.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = -5, b = 8, and c = 2.
Plugging in these values, we have:
x = (-(8) ± √((8)^2 - 4(-5)(2))) / (2(-5))
Simplifying further:
x = (-8 ± √(64 + 40)) / (-10)
x = (-8 ± √(104)) / (-10)
The value inside the square root is 104, which can be simplified as:
x = (-8 ± 2√(26)) / (-10)
This can be further simplified by dividing both the numerator and denominator by -2:
x = (4 ± √(26)) / 5
Therefore, the correct answer when solving the equation −5x^2 + 2 + 8x = 0 using the quadratic formula is:
x = (4 ± √(26)) / 5.