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Simplifying 72 = 1.76x2 + -13.32x + 41 Reorder the terms: 72 = 41 + -13.32x + 1.76x2 Solving 72 = 41 + -13.32x + 1.76x2 Solving for variable 'x'. Combine like terms: 72 + -41 = 31 31 + 13.32x + -1.76x2 = 41 + -13.32x + 1.76x2 + -41 + 13.32x + -1.76x2 Reorder the terms: 31 + 13.32x + -1.76x2 = 41 + -41 + -13.32x + 13.32x + 1.76x2 + -1.76x2 Combine like terms: 41 + -41 = 0 31 + 13.32x + -1.76x2 = 0 + -13.32x + 13.32x + 1.76x2 + -1.76x2 31 + 13.32x + -1.76x2 = -13.32x + 13.32x + 1.76x2 + -1.76x2 Combine like terms: -13.32x + 13.32x = 0.00 31 + 13.32x + -1.76x2 = 0.00 + 1.76x2 + -1.76x2 31 + 13.32x + -1.76x2 = 1.76x2 + -1.76x2 Combine like terms: 1.76x2 + -1.76x2 = 0.00 31 + 13.32x + -1.76x2 = 0.00 Begin completing the square. Divide all terms by -1.76 the coefficient of the squared term: Divide each side by '-1.76'. -17.61363636 + -7.568181818x + x2 = 0 Move the constant term to the right: Add '17.61363636' to each side of the equation. -17.61363636 + -7.568181818x + 17.61363636 + x2 = 0 + 17.61363636 Reorder the terms: -17.61363636 + 17.61363636 + -7.568181818x + x2 = 0 + 17.61363636 Combine like terms: -17.61363636 + 17.61363636 = 0.00000000 0.00000000 + -7.568181818x + x2 = 0 + 17.61363636 -7.568181818x + x2 = 0 + 17.61363636 Combine like terms: 0 + 17.61363636 = 17.61363636 -7.568181818x + x2 = 17.61363636 The x term is -7.568181818x. Take half its coefficient (-3.784090909). Square it (14.31934401) and add it to both sides. Add '14.31934401' to each side of the equation. -7.568181818x + 14.31934401 + x2 = 17.61363636 + 14.31934401 Reorder the terms: 14.31934401 + -7.568181818x + x2 = 17.61363636 + 14.31934401 Combine like terms: 17.61363636 + 14.31934401 = 31.93298037 14.31934401 + -7.568181818x + x2 = 31.93298037 Factor a perfect square on the left side: (x + -3.784090909)(x + -3.784090909) = 31.93298037 Calculate the square root of the right side: 5.65092739 Break this problem into two subproblems by setting (x + -3.784090909) equal to 5.65092739 and -5.65092739.Subproblem 1
x + -3.784090909 = 5.65092739 Simplifying x + -3.784090909 = 5.65092739 Reorder the terms: -3.784090909 + x = 5.65092739 Solving -3.784090909 + x = 5.65092739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.784090909' to each side of the equation. -3.784090909 + 3.784090909 + x = 5.65092739 + 3.784090909 Combine like terms: -3.784090909 + 3.784090909 = 0.000000000 0.000000000 + x = 5.65092739 + 3.784090909 x = 5.65092739 + 3.784090909 Combine like terms: 5.65092739 + 3.784090909 = 9.435018299 x = 9.435018299 Simplifying x = 9.435018299Subproblem 2
x + -3.784090909 = -5.65092739 Simplifying x + -3.784090909 = -5.65092739 Reorder the terms: -3.784090909 + x = -5.65092739 Solving -3.784090909 + x = -5.65092739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.784090909' to each side of the equation. -3.784090909 + 3.784090909 + x = -5.65092739 + 3.784090909 Combine like terms: -3.784090909 + 3.784090909 = 0.000000000 0.000000000 + x = -5.65092739 + 3.784090909 x = -5.65092739 + 3.784090909 Combine like terms: -5.65092739 + 3.784090909 = -1.866836481 x = -1.866836481 Simplifying x = -1.866836481Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.435018299, -1.866836481}
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