Use the quadratic formula to solve the equation:
2x^2=-5x-7
2x^2 + 5x + 7 = 0
Just do it.
To solve the quadratic equation 2x^2 = -5x - 7 using the quadratic formula, we first need to rearrange the equation in standard quadratic form, which is ax^2 + bx + c = 0.
In this case, the equation is already in standard form with a = 2, b = -5, and c = -7.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from our equation, we get:
x = (-(-5) ± √((-5)^2 - 4(2)(-7))) / (2(2))
Simplifying further:
x = (5 ± √(25 + 56)) / 4
x = (5 ± √(81)) / 4
Taking the square root of 81, we have:
x = (5 ± 9) / 4
This leads to two solutions:
x1 = (5 + 9) / 4 --> x1 = 14 / 4 --> x1 = 3.5
x2 = (5 - 9) / 4 --> x2 = -4 / 4 --> x2 = -1
Therefore, the solutions to the equation 2x^2 = -5x - 7 are x = 3.5 and x = -1.