Question

Rewrite the equation by completing the square.
x2 + 10x + 25 = 0

Answer 1

x=−5

Explanation:

Subtract 2525 from both sides of the equation.

x2+10x=−25x2+10x=-25

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of bb.

(b2)2=(5)2(b2)2=(5)2

Add the term to each side of the equation.

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

Simplify the equation.

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Raise 55 to the power of 22.

x2+10x+25=−25+(5)2x2+10x+25=-25+(5)2

Simplify −25+(5)2-25+(5)2.

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x2+10x+25=0x2+10x+25=0

Factor the perfect trinomial square into (x+5)2(x+5)2.

(x+5)2=0(x+5)2=0

Set x+5x+5 equal to 00 and solve for xx.

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Set the factor equal to 00.

x+5=0x+5=0

Subtract 55 from both sides of the equation.

x=−5

Answer 2

( x + 5 )^2 = 0

Explanation:

The left side of the equation is already a perfect square trinomial. The coefficient of our x term is 10, half of it is 5, and squaring it gives us 25 our constant term.

Thus, we can rewrite the left side of the equation as a squared term.

( x + 5 )^2 = 0