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Solve by completing the square:
-7x = 5 - x^2
:
We want to build a quadratic equation on the left. Add x^2 to both sides:
x^2 - 7x + ___ = 5
:
We want to add the value of the 3rd term to make it a perfect square:
Divide the middle term coefficient by 2 and square it: (7/2)^2 = 49/4:
:
x^2 - 7x + 49/4 = 5 + 49/4, we have to add 49/4 to both sides:
x^2 - 7x + 49/4 = 20/4 + 49/4, add like fractions (5 = 20/4)
x^2 - 7x + 49/4 = 69/4
:
x^2 - 7x + 49/4 is (x - 7/2) squared so we have:
(x - 7/2)^2 = 69/4
:
Take the square root of both sides:
x - 7/2 = +/-SqRt(69/4)
:
Adde 7/2 to both sides:
x = +7/2 +/-SqRt(69/4)
x = +7/2 +/- (1/2)SqRt(69) extract the sqrt of 1/4 which is 1/2
:
Two solutions:
x =
and
x =
:
Do you understand the procedure? Any questions?
