Rewrite by completing the square.
2x^2 - 12x + 11
2 x ^ 2 - 12 x + 11 =
2 ( x ^ 2 - 6 x ) + 11 =
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Take one half of the coefficient of x and square it.
In this case : [ ( 1 / 2 ) * 6 ] ^ 2 = 3 ^ 2 = 9
Multiply by 2
2 * 9 = 18
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2 ( x ^ 2 - 6 x + 9 ) + 11 - 18 =
2 ( x ^ 2 - 6 x + 9 ) - 7 =
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Exspress x ^ 2 - 6 x + 9 as a square:
x ^ 2 - 6 x + 9 = ( x - 3 ) ^ 2
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2 ( x - 3 ) ^ 2 - 7
2x^2 - 12x + 11
2(x^2 - 6x) + 11
2(x^2 - 6x + 9) + 11 - 2*9
2(x-3)^2 - 7
To rewrite the quadratic expression 2x^2 - 12x + 11 by completing the square, follow these steps:
Step 1: Verify that the coefficient of the x^2 term is 1 (which is already the case in this expression).
Step 2: Move the constant term (in this case, 11) to the right side of the equation.
2x^2 - 12x = -11
Step 3: We need to "complete the square" by adding and subtracting the square of half the coefficient of the x term. In this case, the coefficient of the x term is -12. Half of -12 is -6, and the square of -6 is 36. So, we add and subtract 36 into the expression.
2x^2 - 12x + 36 - 36 = -11
Step 4: Rearrange the first three terms and factor the perfect square trinomial (x^2 - 6x + 36).
(2x^2 - 12x + 36) - 36 = -11
2(x^2 - 6x + 36) - 36 = -11
Step 5: Factor the perfect square trinomial (x^2 - 6x + 36) into (x - 6)^2.
2(x - 6)^2 - 36 = -11
Now, we have rewritten the quadratic expression 2x^2 - 12x + 11 as 2(x - 6)^2 - 36 = -11.