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Simplifying 0 = -16x2 + 29x + -12 Reorder the terms: 0 = -12 + 29x + -16x2 Solving 0 = -12 + 29x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 12 = 12 12 + -29x + 16x2 = -12 + 29x + -16x2 + 12 + -29x + 16x2 Reorder the terms: 12 + -29x + 16x2 = -12 + 12 + 29x + -29x + -16x2 + 16x2 Combine like terms: -12 + 12 = 0 12 + -29x + 16x2 = 0 + 29x + -29x + -16x2 + 16x2 12 + -29x + 16x2 = 29x + -29x + -16x2 + 16x2 Combine like terms: 29x + -29x = 0 12 + -29x + 16x2 = 0 + -16x2 + 16x2 12 + -29x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 12 + -29x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.75 + -1.8125x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -1.8125x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -1.8125x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -1.8125x + x2 = 0 + -0.75 -1.8125x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -1.8125x + x2 = -0.75 The x term is -1.8125x. Take half its coefficient (-0.90625). Square it (0.8212890625) and add it to both sides. Add '0.8212890625' to each side of the equation. -1.8125x + 0.8212890625 + x2 = -0.75 + 0.8212890625 Reorder the terms: 0.8212890625 + -1.8125x + x2 = -0.75 + 0.8212890625 Combine like terms: -0.75 + 0.8212890625 = 0.0712890625 0.8212890625 + -1.8125x + x2 = 0.0712890625 Factor a perfect square on the left side: (x + -0.90625)(x + -0.90625) = 0.0712890625 Calculate the square root of the right side: 0.267000117 Break this problem into two subproblems by setting (x + -0.90625) equal to 0.267000117 and -0.267000117.Subproblem 1
x + -0.90625 = 0.267000117 Simplifying x + -0.90625 = 0.267000117 Reorder the terms: -0.90625 + x = 0.267000117 Solving -0.90625 + x = 0.267000117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + x = 0.267000117 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + x = 0.267000117 + 0.90625 x = 0.267000117 + 0.90625 Combine like terms: 0.267000117 + 0.90625 = 1.173250117 x = 1.173250117 Simplifying x = 1.173250117Subproblem 2
x + -0.90625 = -0.267000117 Simplifying x + -0.90625 = -0.267000117 Reorder the terms: -0.90625 + x = -0.267000117 Solving -0.90625 + x = -0.267000117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + x = -0.267000117 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + x = -0.267000117 + 0.90625 x = -0.267000117 + 0.90625 Combine like terms: -0.267000117 + 0.90625 = 0.639249883 x = 0.639249883 Simplifying x = 0.639249883Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.173250117, 0.639249883}
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