How do you solve x2+10x+24=0 using completing the square?

3 Answers
George C.
Jun 14, 2015

0=x2+10x+24=(x+5)2−1

Hence x=−5±√1=−5±1

Explanation:

(x+5)2=x2+10x+25

So we have:

0=x2+10x+24=(x+5)2−1

Add 1 to both ends to get:

(x+5)2=1

So:

x+5=±√1=±1

Subtract 5 from both sides to get:

x=−5±1

That is x=−6 or x=−4

Nghi N.
Jun 14, 2015

Factor y=x2+10x+24 by completing the square

Explanation:

y=x210x+(25−25)+24=0
y=(x+5)2−1=0
(x+5)2=1 -> x+5=±1

x = -5 + 1 = -4
x = -5 - 1 = -6

Meave60
Jun 14, 2015

Create a perfect square trinomial on the left side of the equation, then factor it and solve for x. The general equation for a perfect square trinomial is a2+2ab+b2=(a+b)2.

Explanation:

x2+10x+24=0

We are going to create a perfect square trinomial on the left side of the equation, then solve for x. The general equation for a perfect square trinomial is a2+2ab+b2=(a+b)2.

Subtract 24 from both sides.

x2+10x=−24

Divide the coefficient of the x term by 2, then square the result, and add it to both sides.

102=5 ;52=25

x2+10x+25=−24+25 =

x2+10x+25=1

We now have a perfect square trinomial on the left side, in which a=xandb=5. Factor the trinomial, then solve for x.

(x+5)2=1

Take the square root of both sides.

x+5=±√1 =

x=±√1−5 =

x=√1−5=1−5=−4

x=−√1−5=−1−5=−6

x=−4
x=−6

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