Question 666507
{{{x^2 + 2x = 5}}}
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No, you are not supposed to set this equal to zero when you complete the square; that is for quadratic formula. It is in perfect starting format the way it is -- the coefficient of {{{x^2}}} (number it is multiplied; for example, the coefficient of x in 2x is 2) is 1, which is exactly what you want. Also, the two x terms (x^2 and 2x) are on the left of the equation, and the 5 is on the right, which is also correct.
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Divide the coefficient of the "x" term (in this case, the x term would be 2x, so its coefficient would be the number before the x, 2) in half. This would give you {{{2/2}}}, or 1.
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Square this number: {{{1^2}}} = 1
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Add the result to both sides of the equation: {{{x^2 + 2x + 1 = 5 + 1}}}
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Simplify the right side of the equation: {{{x^2 + 2x + 1 = 6}}}
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Factor the left side of the equation: {{{(x + 1)^2 = 6}}}
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Square root both sides. Remember that the right side could be either the positive or the negative square root: x + 1 = ±{{{sqrt(6)}}}
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Isolate the x by subtracting 1 from both sides: x = -1 ± {{{sqrt(6)}}}
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Your final answer is x = -1 ± {{{sqrt(6)}}}.