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Simplifying -200x + -1x2 = 65x + 3150 Reorder the terms: -200x + -1x2 = 3150 + 65x Solving -200x + -1x2 = 3150 + 65x Solving for variable 'x'. Reorder the terms: -3150 + -200x + -65x + -1x2 = 3150 + 65x + -3150 + -65x Combine like terms: -200x + -65x = -265x -3150 + -265x + -1x2 = 3150 + 65x + -3150 + -65x Reorder the terms: -3150 + -265x + -1x2 = 3150 + -3150 + 65x + -65x Combine like terms: 3150 + -3150 = 0 -3150 + -265x + -1x2 = 0 + 65x + -65x -3150 + -265x + -1x2 = 65x + -65x Combine like terms: 65x + -65x = 0 -3150 + -265x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3150 + 265x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3150 + 265x + x2)' equal to zero and attempt to solve: Simplifying 3150 + 265x + x2 = 0 Solving 3150 + 265x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3150' to each side of the equation. 3150 + 265x + -3150 + x2 = 0 + -3150 Reorder the terms: 3150 + -3150 + 265x + x2 = 0 + -3150 Combine like terms: 3150 + -3150 = 0 0 + 265x + x2 = 0 + -3150 265x + x2 = 0 + -3150 Combine like terms: 0 + -3150 = -3150 265x + x2 = -3150 The x term is 265x. Take half its coefficient (132.5). Square it (17556.25) and add it to both sides. Add '17556.25' to each side of the equation. 265x + 17556.25 + x2 = -3150 + 17556.25 Reorder the terms: 17556.25 + 265x + x2 = -3150 + 17556.25 Combine like terms: -3150 + 17556.25 = 14406.25 17556.25 + 265x + x2 = 14406.25 Factor a perfect square on the left side: (x + 132.5)(x + 132.5) = 14406.25 Calculate the square root of the right side: 120.026038842 Break this problem into two subproblems by setting (x + 132.5) equal to 120.026038842 and -120.026038842.Subproblem 1
x + 132.5 = 120.026038842 Simplifying x + 132.5 = 120.026038842 Reorder the terms: 132.5 + x = 120.026038842 Solving 132.5 + x = 120.026038842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-132.5' to each side of the equation. 132.5 + -132.5 + x = 120.026038842 + -132.5 Combine like terms: 132.5 + -132.5 = 0.0 0.0 + x = 120.026038842 + -132.5 x = 120.026038842 + -132.5 Combine like terms: 120.026038842 + -132.5 = -12.473961158 x = -12.473961158 Simplifying x = -12.473961158Subproblem 2
x + 132.5 = -120.026038842 Simplifying x + 132.5 = -120.026038842 Reorder the terms: 132.5 + x = -120.026038842 Solving 132.5 + x = -120.026038842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-132.5' to each side of the equation. 132.5 + -132.5 + x = -120.026038842 + -132.5 Combine like terms: 132.5 + -132.5 = 0.0 0.0 + x = -120.026038842 + -132.5 x = -120.026038842 + -132.5 Combine like terms: -120.026038842 + -132.5 = -252.526038842 x = -252.526038842 Simplifying x = -252.526038842Solution
The solution to the problem is based on the solutions from the subproblems. x = {-12.473961158, -252.526038842}Solution
x = {-12.473961158, -252.526038842}
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