Solve. Find the exact solution(s). Simplify as much as possible. Show work.
2x^2 + 4x – 1 = 0
2x^2 + 4x – 1 = 0
I would use the quadratic equation.
To solve the equation 2x^2 + 4x - 1 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solution for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, the equation is 2x^2 + 4x - 1 = 0, so a = 2, b = 4, and c = -1. Plugging these values into the quadratic formula, we get:
x = (-4 ± √(4^2 - 4 * 2 * -1)) / (2 * 2)
Simplifying further:
x = (-4 ± √(16 + 8)) / 4
x = (-4 ± √24) / 4
Now, let's simplify the square root term:
x = (-4 ± √(4 * 6)) / 4
x = (-4 ± 2√6) / 4
We can simplify the expression further by factoring out a common factor of 2 from the numerator:
x = (2(-2 ± √6)) / 4
Now, we can simplify the expression by canceling out the common factor of 2 in the numerator and denominator:
x = (-2 ± √6) / 2
Therefore, the exact solutions for the equation 2x^2 + 4x - 1 = 0 are:
x = (-2 + √6) / 2
x = (-2 - √6) / 2