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Simplifying (3x2) + -3x = 3600 Reorder the terms: -3x + (3x2) = 3600 Solving -3x + (3x2) = 3600 Solving for variable 'x'. Reorder the terms: -3600 + -3x + (3x2) = 3600 + -3600 Combine like terms: 3600 + -3600 = 0 -3600 + -3x + (3x2) = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1200 + -1x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1200 + -1x + x2)' equal to zero and attempt to solve: Simplifying -1200 + -1x + x2 = 0 Solving -1200 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1200' to each side of the equation. -1200 + -1x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + -1x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + -1x + x2 = 0 + 1200 -1x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 -1x + x2 = 1200 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1200 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1200 + 0.25 Combine like terms: 1200 + 0.25 = 1200.25 0.25 + -1x + x2 = 1200.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1200.25 Calculate the square root of the right side: 34.644624403 Break this problem into two subproblems by setting (x + -0.5) equal to 34.644624403 and -34.644624403.Subproblem 1
x + -0.5 = 34.644624403 Simplifying x + -0.5 = 34.644624403 Reorder the terms: -0.5 + x = 34.644624403 Solving -0.5 + x = 34.644624403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 34.644624403 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 34.644624403 + 0.5 x = 34.644624403 + 0.5 Combine like terms: 34.644624403 + 0.5 = 35.144624403 x = 35.144624403 Simplifying x = 35.144624403Subproblem 2
x + -0.5 = -34.644624403 Simplifying x + -0.5 = -34.644624403 Reorder the terms: -0.5 + x = -34.644624403 Solving -0.5 + x = -34.644624403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -34.644624403 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -34.644624403 + 0.5 x = -34.644624403 + 0.5 Combine like terms: -34.644624403 + 0.5 = -34.144624403 x = -34.144624403 Simplifying x = -34.144624403Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.144624403, -34.144624403}Solution
x = {35.144624403, -34.144624403}
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