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Mumz [18]
3 years ago
14

Which of the following correctly completes the the square for the equation below? x^2+18x=0

Mathematics
2 answers:
Nookie1986 [14]3 years ago
4 0
X² +18x = 0

To complete the square we are going to use formula a² +2ab +b² = (a+b)²

x² +2*9*x = 0
x² +2*9x+9² = 9²
(x+9)² = 9²
√(x+9)² = +/-√9²
x+9 = 9, or x+9 = -9
x=0, or x= - 18

The equation could be solved different way
x² +18x = 0
x(x+18) = 0
x=0 or x+18=0
x=0 or x=-18

My name is Ann [436]3 years ago
3 0
We know that a perfect square has the form
(x+y)^2 = x^2+2xy+y^2
If we substitute the numbers in the given equation, we have 
(x+y)^2 = x^2+2xy+y^2 = x^2+2x(9) + y^2
By comparison of the coefficients of the term xy, we have y=9, hence we need y^2=9^2=81 to complete the square. 

The completed square would be
(x+9)^2-81=0  (which expands back to x^2+18x=0)

However, if the objective is to solve the equation, I would solve it by factoring, i.e. 
x^2+18x=0 => x(x+18)=0 => x=0 or x=-18
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<h3>Answer: Yes they are equivalent</h3>

==============================================

Work Shown:

Expand out the first expression to get

(a-3)(2a^2 + 3a + 3)

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