What number is used to complete the square for the equation x^2 + 5x = 0?
a) 25
b) 6.25
c) 2.5
d) 10
d
(d) is not correct.
When we need to complete the square of an expression, we examine the coefficients of the x² and x terms.
To complete the square of a general quadratic equation
ax²+bx+c
we first rewrite it as:
a(x² + (b/a)x + c/a)
to make the coefficient of x² equal to 1.0 inside the parentheses.
After that, we regroup the terms as
a( (x+(b/2a))² + c/a - (b/2a)² )
Therefore the number to complete the square is b/2 if a=1.
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