Question 313256: solve for x: x^2+6x+5>10
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve for x:
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x^2+6x+5>10
Rearrange:
x^2 + 6x -5 > 0
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1st: Solve the EQUALITY:
x^2+6x-5 = 0
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x = [-6 +- sqrt(36 - 4*-5)]/2
x = [-6 +- sqrt(56)]/2
x = [-6 +- 2sqrt(14)]/2
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x = [-3+sqrt(14)] or x = [-3-sqrt(14)]
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Approximate answers: x = -6.74 or x = 0.74
Note: these are NOT solutions for the INEQUALITY, which is your problem.
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2nd: Solve the INEQUALITY x^2 + 6x -5 > 0
Draw a number line and mark x = -6.74 or x = 0.74
Check a sample value from each of the intervals in the INEQULITY.
If x = -10, (-10)^2+6(-10)-5 > 0 ; true so solutions in (-inf,-6.74)
If x = 0, (0)^2+6(0)-5 > 0 ; false so no solutions in (-6.74,0.74)
If x = 10, (10)^2+6*10-5 > 0 ; true so solutions in (0.74,+inf)
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Cheers,
Stan H.
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