solve for x: x^2-5x-6=0
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which two factors of 6 differ by 5?
3+2
"differ by" -- I think you need to learn the meaning of that term.
How about 1 and 6?
-6 + 1 = -5
That help?
To solve the quadratic equation x^2-5x-6=0, we can use the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 1, b = -5, and c = -6. Plugging these values into the quadratic formula, we get:
x = (-(-5) ± √((-5)^2 - 4(1)(-6))) / (2(1))
Simplifying further, we have:
x = (5 ± √(25 + 24)) / 2
x = (5 ± √49) / 2
x = (5 ± 7) / 2
So, the two solutions for x are:
x = (5 + 7) / 2 = 6
x = (5 - 7) / 2 = -1
Therefore, the values of x that satisfy the quadratic equation x^2 - 5x - 6 = 0 are x = 6 and x = -1.