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Simplifying 100 = -16x2 + 88x + 18 Reorder the terms: 100 = 18 + 88x + -16x2 Solving 100 = 18 + 88x + -16x2 Solving for variable 'x'. Combine like terms: 100 + -18 = 82 82 + -88x + 16x2 = 18 + 88x + -16x2 + -18 + -88x + 16x2 Reorder the terms: 82 + -88x + 16x2 = 18 + -18 + 88x + -88x + -16x2 + 16x2 Combine like terms: 18 + -18 = 0 82 + -88x + 16x2 = 0 + 88x + -88x + -16x2 + 16x2 82 + -88x + 16x2 = 88x + -88x + -16x2 + 16x2 Combine like terms: 88x + -88x = 0 82 + -88x + 16x2 = 0 + -16x2 + 16x2 82 + -88x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 82 + -88x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(41 + -44x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(41 + -44x + 8x2)' equal to zero and attempt to solve: Simplifying 41 + -44x + 8x2 = 0 Solving 41 + -44x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 5.125 + -5.5x + x2 = 0 Move the constant term to the right: Add '-5.125' to each side of the equation. 5.125 + -5.5x + -5.125 + x2 = 0 + -5.125 Reorder the terms: 5.125 + -5.125 + -5.5x + x2 = 0 + -5.125 Combine like terms: 5.125 + -5.125 = 0.000 0.000 + -5.5x + x2 = 0 + -5.125 -5.5x + x2 = 0 + -5.125 Combine like terms: 0 + -5.125 = -5.125 -5.5x + x2 = -5.125 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -5.125 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -5.125 + 7.5625 Combine like terms: -5.125 + 7.5625 = 2.4375 7.5625 + -5.5x + x2 = 2.4375 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 2.4375 Calculate the square root of the right side: 1.5612495 Break this problem into two subproblems by setting (x + -2.75) equal to 1.5612495 and -1.5612495.Subproblem 1
x + -2.75 = 1.5612495 Simplifying x + -2.75 = 1.5612495 Reorder the terms: -2.75 + x = 1.5612495 Solving -2.75 + x = 1.5612495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 1.5612495 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 1.5612495 + 2.75 x = 1.5612495 + 2.75 Combine like terms: 1.5612495 + 2.75 = 4.3112495 x = 4.3112495 Simplifying x = 4.3112495Subproblem 2
x + -2.75 = -1.5612495 Simplifying x + -2.75 = -1.5612495 Reorder the terms: -2.75 + x = -1.5612495 Solving -2.75 + x = -1.5612495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -1.5612495 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -1.5612495 + 2.75 x = -1.5612495 + 2.75 Combine like terms: -1.5612495 + 2.75 = 1.1887505 x = 1.1887505 Simplifying x = 1.1887505Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.3112495, 1.1887505}Solution
x = {4.3112495, 1.1887505}
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