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Simplifying 18 = 1.76x2 + -13.32x + 41 Reorder the terms: 18 = 41 + -13.32x + 1.76x2 Solving 18 = 41 + -13.32x + 1.76x2 Solving for variable 'x'. Combine like terms: 18 + -41 = -23 -23 + 13.32x + -1.76x2 = 41 + -13.32x + 1.76x2 + -41 + 13.32x + -1.76x2 Reorder the terms: -23 + 13.32x + -1.76x2 = 41 + -41 + -13.32x + 13.32x + 1.76x2 + -1.76x2 Combine like terms: 41 + -41 = 0 -23 + 13.32x + -1.76x2 = 0 + -13.32x + 13.32x + 1.76x2 + -1.76x2 -23 + 13.32x + -1.76x2 = -13.32x + 13.32x + 1.76x2 + -1.76x2 Combine like terms: -13.32x + 13.32x = 0.00 -23 + 13.32x + -1.76x2 = 0.00 + 1.76x2 + -1.76x2 -23 + 13.32x + -1.76x2 = 1.76x2 + -1.76x2 Combine like terms: 1.76x2 + -1.76x2 = 0.00 -23 + 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'. 13.06818182 + -7.568181818x + x2 = 0 Move the constant term to the right: Add '-13.06818182' to each side of the equation. 13.06818182 + -7.568181818x + -13.06818182 + x2 = 0 + -13.06818182 Reorder the terms: 13.06818182 + -13.06818182 + -7.568181818x + x2 = 0 + -13.06818182 Combine like terms: 13.06818182 + -13.06818182 = 0.00000000 0.00000000 + -7.568181818x + x2 = 0 + -13.06818182 -7.568181818x + x2 = 0 + -13.06818182 Combine like terms: 0 + -13.06818182 = -13.06818182 -7.568181818x + x2 = -13.06818182 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 = -13.06818182 + 14.31934401 Reorder the terms: 14.31934401 + -7.568181818x + x2 = -13.06818182 + 14.31934401 Combine like terms: -13.06818182 + 14.31934401 = 1.25116219 14.31934401 + -7.568181818x + x2 = 1.25116219 Factor a perfect square on the left side: (x + -3.784090909)(x + -3.784090909) = 1.25116219 Calculate the square root of the right side: 1.118553615 Break this problem into two subproblems by setting (x + -3.784090909) equal to 1.118553615 and -1.118553615.Subproblem 1
x + -3.784090909 = 1.118553615 Simplifying x + -3.784090909 = 1.118553615 Reorder the terms: -3.784090909 + x = 1.118553615 Solving -3.784090909 + x = 1.118553615 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 = 1.118553615 + 3.784090909 Combine like terms: -3.784090909 + 3.784090909 = 0.000000000 0.000000000 + x = 1.118553615 + 3.784090909 x = 1.118553615 + 3.784090909 Combine like terms: 1.118553615 + 3.784090909 = 4.902644524 x = 4.902644524 Simplifying x = 4.902644524Subproblem 2
x + -3.784090909 = -1.118553615 Simplifying x + -3.784090909 = -1.118553615 Reorder the terms: -3.784090909 + x = -1.118553615 Solving -3.784090909 + x = -1.118553615 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 = -1.118553615 + 3.784090909 Combine like terms: -3.784090909 + 3.784090909 = 0.000000000 0.000000000 + x = -1.118553615 + 3.784090909 x = -1.118553615 + 3.784090909 Combine like terms: -1.118553615 + 3.784090909 = 2.665537294 x = 2.665537294 Simplifying x = 2.665537294Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.902644524, 2.665537294}
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