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Simplifying 9x2 + -136x + 200 = 0 Reorder the terms: 200 + -136x + 9x2 = 0 Solving 200 + -136x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 22.22222222 + -15.11111111x + x2 = 0 Move the constant term to the right: Add '-22.22222222' to each side of the equation. 22.22222222 + -15.11111111x + -22.22222222 + x2 = 0 + -22.22222222 Reorder the terms: 22.22222222 + -22.22222222 + -15.11111111x + x2 = 0 + -22.22222222 Combine like terms: 22.22222222 + -22.22222222 = 0.00000000 0.00000000 + -15.11111111x + x2 = 0 + -22.22222222 -15.11111111x + x2 = 0 + -22.22222222 Combine like terms: 0 + -22.22222222 = -22.22222222 -15.11111111x + x2 = -22.22222222 The x term is -15.11111111x. Take half its coefficient (-7.555555555). Square it (57.08641974) and add it to both sides. Add '57.08641974' to each side of the equation. -15.11111111x + 57.08641974 + x2 = -22.22222222 + 57.08641974 Reorder the terms: 57.08641974 + -15.11111111x + x2 = -22.22222222 + 57.08641974 Combine like terms: -22.22222222 + 57.08641974 = 34.86419752 57.08641974 + -15.11111111x + x2 = 34.86419752 Factor a perfect square on the left side: (x + -7.555555555)(x + -7.555555555) = 34.86419752 Calculate the square root of the right side: 5.904591224 Break this problem into two subproblems by setting (x + -7.555555555) equal to 5.904591224 and -5.904591224.Subproblem 1
x + -7.555555555 = 5.904591224 Simplifying x + -7.555555555 = 5.904591224 Reorder the terms: -7.555555555 + x = 5.904591224 Solving -7.555555555 + x = 5.904591224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.555555555' to each side of the equation. -7.555555555 + 7.555555555 + x = 5.904591224 + 7.555555555 Combine like terms: -7.555555555 + 7.555555555 = 0.000000000 0.000000000 + x = 5.904591224 + 7.555555555 x = 5.904591224 + 7.555555555 Combine like terms: 5.904591224 + 7.555555555 = 13.460146779 x = 13.460146779 Simplifying x = 13.460146779Subproblem 2
x + -7.555555555 = -5.904591224 Simplifying x + -7.555555555 = -5.904591224 Reorder the terms: -7.555555555 + x = -5.904591224 Solving -7.555555555 + x = -5.904591224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.555555555' to each side of the equation. -7.555555555 + 7.555555555 + x = -5.904591224 + 7.555555555 Combine like terms: -7.555555555 + 7.555555555 = 0.000000000 0.000000000 + x = -5.904591224 + 7.555555555 x = -5.904591224 + 7.555555555 Combine like terms: -5.904591224 + 7.555555555 = 1.650964331 x = 1.650964331 Simplifying x = 1.650964331Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.460146779, 1.650964331}
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