How do you solve using the completing the square method x^2 + 10x + 14 = -7x2+10x+14=−7?

1 Answer
Ken C.
Jul 8, 2016

See below.

Explanation:

The first thing you'll want to do is take the constant terms and put them to one side of the equation. In this case, that means subtracting 1414 from both sides:
x^2+10x=-7-14x2+10x=−7−14
->x^2+10x=-21→x2+10x=−21

Now you want to take half of the xx term, square it, and add it to both sides. That means taking half of ten, which is 55, squaring it, which makes 2525, and adding it to both sides:
x^2+10x+(10/2)^2=-21+(10/2)^2x2+10x+(102)2=−21+(102)2
->x^2+10x+25=-21+25→x2+10x+25=−21+25

Note that the left side of this equation is a perfect square: it factors into (x+5)^2(x+5)2 (that's why they call it "completing the square"):
(x+5)^2=-21+25(x+5)2=−21+25
->(x+5)^2=4→(x+5)2=4

We can take the square root of both sides:
x+5=+-sqrt(4)x+5=±√4
->x+5=+-2→x+5=±2

And subtract 55 from both sides:
x=+-2-5x=±2−5
->x=+2-5=-3→x=+2−5=−3 and x=-2-5=-7x=−2−5=−7

Our solutions are therefore x=-3x=−3 and x=-7x=−7.

Related questions
See all questions in Completing the Square
Impact of this question
3461 views around the world
You can reuse this answer
Creative Commons License