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How do you complete the square by filling in the two blanks so as to produce a true equation.

x^2 - 12x + ---- = (x - -----)^2

  • algebra -

    The first blank will have a 36 in it. The second blank will have 6 in it.

    When you complete the square in this format, take half of the number in front of x, (called coefficient), and square it. So, in your case, the number in front of x is -12. If I take half of it, it is -6. Then, if I square it, the final result is +36. That goes in the first blank completing the trinomial on the left --> x^2 - 12x + 36

    Now, the squared binomial on the right will use the half of the coefficient value. Thus, (x-6)^2 is the final answer on the right.

    If you want to check your result, take the (x-6)^2 binomial, and rewrite it as a repeated factor: (x-6)(x-6). Perform FOIL, and you should get x^2 - 12x + 36.

    WARNING: Completing the Square only works when the coefficient of the x^2 term is ONE!

    Hope this helps!

  • algebra -

    Yes you helped me a lot. Thank you for showing me in steps how to solve this question

  • algebra 1 -

    x^2-18x+___=( )^2

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