How do you solve using the completing the square method #x^2 + 10x + 16 = 0#?

Answer 1

#x=-2# and #x=-8#

To solve the equation #x^2+10x+16=0# using the completing square method, as coefficient of #x^2# is #1# and independent term #16# positive, we have to identify factors of #16# whose sum is #10#, coefficient of #x# term.

These are #2# and #8# and hence we should split the equation as follows:

#x^2+2x+8x+16=0# or #x(x+2)+8(x+2)=0# i.e.

#(x+2)(x+8)=0#.

Hence either #x+2=0# i.e. #x=-2# or

#x+8=0# i.e. #x=-8#

[In general if equation is in form #ax^2+bx+c=0#, one should identify two factors whose product is #a*c# and sum is #b#.]

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Answer 2

Ethan Adkins

To solve using the completing the square method, first move the constant term to the other side of the equation, then add and subtract the square of half the coefficient of x. Next, factor the perfect square trinomial, and solve for x.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.