SOLUTION: solve x^2 is greater than or equal to 7+3x

Question 290408: solve
x^2 is greater than or equal to 7+3x
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
solve
x^2 is greater than or equal to 7+3x
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x^2 >= 7+3x
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Solve the Equality which is the boundary of the inequality.
Solve x^2 - 3x - 7 = 0
x = [3 +- sqrt(9 -4*1*-7)]/2
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x = [3 +- sqrt(37)]/2
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x = 4.54.. or x = -1.54..
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Mark those points on a number line.
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To solve the inequality, test a check value in
each of the three resulting intervals.
x^2-3x-7 >= 0
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Check x = -2: 4+6-7>0 ; true, so solutions in (-inf,-1.54)
Check x = 0: 0 - 0-7 > 0 ; false
Check x = 5: 25-15-7 > 0 ; true so solutions in (4.54,+inf)
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Cheers,
Stan H.
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