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March 25, 2017

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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

  • algebra - ,

    (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.

    Post if you need further explanations.

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