The first step to solve the given equation, which is a quadratic equation, is to use the quadratic formula. A quadratic equation is an equation that can be written in the form ax^2 + bx + c = 0. We can solve for x by using the quadratic formula, which is given by x = [-b ± sqrt(b^2 - 4ac)] / 2a.
Okay, now that we are scholars, let's solve it!
1. Identify the coefficients a, b, and c in the equation. In our equation, x^(2)-8x-9=0, a=1, b=-8, and c=-9.
2. Substitute the coefficient values into the quadratic formula. We get:
x = [-(-8) ± sqrt((-8)^2 - 4*1*(-9))
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(2*1)
3. Simplify the expression as much as possible. This gives us:
x = [8 ± sqrt(64 + 36)] / 2
= [8 ± sqrt(100)] / 2
= [8 ± 10] / 2
4. Find the two possible solutions for x by breaking the plus-minus operation into two separate calculations (one with plus, the other with minus). This gives us:
x = (8 + 10) / 2 = 18 / 2 = 9
and
x = (8 - 10) / 2 = -2 / 2 = -1
Therefore, the solutions to the equation are x = 9 and x = -1.