Solve for in the equation x2 - 3x - 40 = 0.
it factors ....
(x-8)(x+5) = 0
x = 8 or x = -5
To solve the quadratic equation x^2 - 3x - 40 = 0, we can use the quadratic formula.
The quadratic formula states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 1, b = -3, and c = -40. Plugging these values into the formula, we get:
x = (-(-3) ± √((-3)^2 - 4(1)(-40))) / (2(1))
Simplifying further:
x = (3 ± √(9 + 160)) / 2
x = (3 ± √169) / 2
x = (3 ± 13) / 2
Now we have two possible solutions:
x1 = (3 + 13) / 2 = 16/2 = 8
x2 = (3 - 13) / 2 = -10/2 = -5
So the solutions to the equation x^2 - 3x - 40 = 0 are x = 8 and x = -5.