which expression gives the solutions of –5 + 2x^2 = –6x?
nvm i got it
what was it?
To find the solutions of the equation –5 + 2x^2 = –6x, we can set the equation equal to zero by rearranging the terms:
2x^2 + 6x - 5 = 0
Now, we can solve this quadratic equation to find the values of x. There are multiple ways to do this, but one common method is by factoring or using the quadratic formula.
Since the quadratic equation does not factor easily, we will use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, the values of a, b, and c are as follows:
a = 2, b = 6, c = -5
Plugging these values into the quadratic formula, we have:
x = (-(6) ± √((6)^2 - 4(2)(-5))) / (2(2))
Simplifying further:
x = (-6 ± √(36 + 40)) / 4
x = (-6 ± √(76)) / 4
x = (-6 ± √(4 * 19)) / 4
x = (-6 ± 2√(19)) / 4
Simplifying the expression inside the square root:
x = (-3 ± √(19)) / 2
Therefore, the solutions to the equation –5 + 2x^2 = –6x are:
x = (-3 + √(19)) / 2
x = (-3 - √(19)) / 2