Question 541926: X2+5x-6=0
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! I presume the problem as written means: x^2 + 5x - 6 = 0. I will go from there. This is a basic quadratic equation. The solution method is to:
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simplify all like terms (nothing to do here)
factor the expression
find the solutions to the factored terms
evaluate the solutions as to their relevance to the assigned problem
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x^2 + 5x - 6 = 0
is factored into this:
(x + 6) * (x - 1) = 0
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multiply the expression back out to satisfy yourself you have factored it properly by multiplying each term in each factor against all terms in the other factor:
x * (x - 1) + 6 * (x - 1) = 0
x^2 - x + 6x - 6 = 0
x^2 + 5x - 6 = 0
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In its factored form, it is easy to see that if either term inside the parentheses can be set to zero, then no matter what it is multiplied by, the equation still results in zero.
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If we set x = -6, or 1, then the equation is satisfied. You should go back into the original equation and check your work.
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x = -6:
-6^2 + 5(-6) - 6 = 0
36 - 30 - 6 = 0
0 = 0 checks
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x = 1:
1^2 + 5(1) - 6 = 0
1 + 5 - 6 = 0
0 = 0 checks
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Solutions are x = -6, 1
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cheers,
Lee
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PS. If you need help figuring out how to factor quadratic equations, please feel free to email me: w.lee.meeks@gmail.com
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