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Joanna Lara
Mathematics
4 November, 04:29
3x^2+6x-9=0 complete the square
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Kolten Nicholson
4 November, 04:58
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You could simplify this work by factoring "3" out of all four terms, as follows:
3 (x^2 + 2x - 3) = 3 (0) = 0
Hold the 3 for later re-insertion. Focus on "completing the square" of x^2 + 2x - 3.
1. Take the coefficient (2) of x and halve it: 2 divided by 2 is 1
2. Square this result: 1^2 = 1
3. Add this result (1) to x^2 + 2x, holding the "-3" for later:
x^2 + 2x
4 Subtract (1) from x^2 + 2x + 1: x^2 + 2x + 1 - 3 - 1 = 0,
or x^2 + 2x + 1 - 4 = 0
5. Simplify, remembering that x^2 + 2x + 1 is a perfect square:
(x+1) ^2 - 4 = 0
We have "completed the square." We can stop here. or, we could solve for x: one way would be to factor the left side:
[ (x+1) - 2][ (x+1) + 2]=0 The solutions would then be:
x+1-2=0=> x-1=0, or x=1, and
x+1 + 2 = 0 = > x+3=0, or x=-3. (you were not asked to do this).
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