slove for ^x
x^2-3x-18=0
(x-6)(x+3)
To solve the equation x^2 - 3x - 18 = 0 for x, we can use the quadratic formula. The quadratic formula states that for an 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)
For the given equation x^2 - 3x - 18 = 0, we have a = 1, b = -3, and c = -18. Plugging these values into the quadratic formula, we get:
x = (-(-3) ± √((-3)^2 - 4(1)(-18))) / (2(1))
Simplifying further:
x = (3 ± √(9 + 72)) / 2
x = (3 ± √81) / 2
Since √81 = 9, we can simplify the equation to:
x = (3 ± 9) / 2
This gives us the two possible solutions:
x1 = (3 + 9) / 2 = 12 / 2 = 6
x2 = (3 - 9) / 2 = -6 / 2 = -3
Therefore, the solutions to the equation x^2 - 3x - 18 = 0 are x = 6 and x = -3.