Solve the following quadratic equation using the quadratic formula.
-2x²-7x+13=0
**Note: Make sure to enter both solutions together in the space provided using the ± symbol.
For example: x = {½ ± √10}
x = {______}
To solve the quadratic equation -2x²-7x+13=0 using the quadratic formula, let's first identify the coefficients a, b, and c:
a = -2
b = -7
c = 13
The quadratic formula is given by:
x = (-b ± √(b²-4ac)) / (2a)
Substituting the values of a, b, and c into the formula:
x = (-(-7) ± √((-7)²-4(-2)(13))) / (2(-2))
Simplifying:
x = (7 ± √(49 + 104)) / (-4)
x = (7 ± √153) / (-4)
Therefore, the solutions to the quadratic equation -2x²-7x+13=0 are:
x = (7 + √153) / (-4) and x = (7 - √153) / (-4)
x = {-7 ± √153} / 4