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Simplifying x = 2x2 + -36x + 112 Reorder the terms: x = 112 + -36x + 2x2 Solving x = 112 + -36x + 2x2 Solving for variable 'x'. Reorder the terms: -112 + x + 36x + -2x2 = 112 + -36x + 2x2 + -112 + 36x + -2x2 Combine like terms: x + 36x = 37x -112 + 37x + -2x2 = 112 + -36x + 2x2 + -112 + 36x + -2x2 Reorder the terms: -112 + 37x + -2x2 = 112 + -112 + -36x + 36x + 2x2 + -2x2 Combine like terms: 112 + -112 = 0 -112 + 37x + -2x2 = 0 + -36x + 36x + 2x2 + -2x2 -112 + 37x + -2x2 = -36x + 36x + 2x2 + -2x2 Combine like terms: -36x + 36x = 0 -112 + 37x + -2x2 = 0 + 2x2 + -2x2 -112 + 37x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -112 + 37x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 56 + -18.5x + x2 = 0 Move the constant term to the right: Add '-56' to each side of the equation. 56 + -18.5x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + -18.5x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -18.5x + x2 = 0 + -56 -18.5x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 -18.5x + x2 = -56 The x term is -18.5x. Take half its coefficient (-9.25). Square it (85.5625) and add it to both sides. Add '85.5625' to each side of the equation. -18.5x + 85.5625 + x2 = -56 + 85.5625 Reorder the terms: 85.5625 + -18.5x + x2 = -56 + 85.5625 Combine like terms: -56 + 85.5625 = 29.5625 85.5625 + -18.5x + x2 = 29.5625 Factor a perfect square on the left side: (x + -9.25)(x + -9.25) = 29.5625 Calculate the square root of the right side: 5.437140793 Break this problem into two subproblems by setting (x + -9.25) equal to 5.437140793 and -5.437140793.Subproblem 1
x + -9.25 = 5.437140793 Simplifying x + -9.25 = 5.437140793 Reorder the terms: -9.25 + x = 5.437140793 Solving -9.25 + x = 5.437140793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.25' to each side of the equation. -9.25 + 9.25 + x = 5.437140793 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + x = 5.437140793 + 9.25 x = 5.437140793 + 9.25 Combine like terms: 5.437140793 + 9.25 = 14.687140793 x = 14.687140793 Simplifying x = 14.687140793Subproblem 2
x + -9.25 = -5.437140793 Simplifying x + -9.25 = -5.437140793 Reorder the terms: -9.25 + x = -5.437140793 Solving -9.25 + x = -5.437140793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.25' to each side of the equation. -9.25 + 9.25 + x = -5.437140793 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + x = -5.437140793 + 9.25 x = -5.437140793 + 9.25 Combine like terms: -5.437140793 + 9.25 = 3.812859207 x = 3.812859207 Simplifying x = 3.812859207Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.687140793, 3.812859207}
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