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Simplifying 11000 + -310x + 2x2 = 2900 Solving 11000 + -310x + 2x2 = 2900 Solving for variable 'x'. Reorder the terms: 11000 + -2900 + -310x + 2x2 = 2900 + -2900 Combine like terms: 11000 + -2900 = 8100 8100 + -310x + 2x2 = 2900 + -2900 Combine like terms: 2900 + -2900 = 0 8100 + -310x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4050 + -155x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4050 + -155x + x2)' equal to zero and attempt to solve: Simplifying 4050 + -155x + x2 = 0 Solving 4050 + -155x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4050' to each side of the equation. 4050 + -155x + -4050 + x2 = 0 + -4050 Reorder the terms: 4050 + -4050 + -155x + x2 = 0 + -4050 Combine like terms: 4050 + -4050 = 0 0 + -155x + x2 = 0 + -4050 -155x + x2 = 0 + -4050 Combine like terms: 0 + -4050 = -4050 -155x + x2 = -4050 The x term is -155x. Take half its coefficient (-77.5). Square it (6006.25) and add it to both sides. Add '6006.25' to each side of the equation. -155x + 6006.25 + x2 = -4050 + 6006.25 Reorder the terms: 6006.25 + -155x + x2 = -4050 + 6006.25 Combine like terms: -4050 + 6006.25 = 1956.25 6006.25 + -155x + x2 = 1956.25 Factor a perfect square on the left side: (x + -77.5)(x + -77.5) = 1956.25 Calculate the square root of the right side: 44.229515032 Break this problem into two subproblems by setting (x + -77.5) equal to 44.229515032 and -44.229515032.Subproblem 1
x + -77.5 = 44.229515032 Simplifying x + -77.5 = 44.229515032 Reorder the terms: -77.5 + x = 44.229515032 Solving -77.5 + x = 44.229515032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '77.5' to each side of the equation. -77.5 + 77.5 + x = 44.229515032 + 77.5 Combine like terms: -77.5 + 77.5 = 0.0 0.0 + x = 44.229515032 + 77.5 x = 44.229515032 + 77.5 Combine like terms: 44.229515032 + 77.5 = 121.729515032 x = 121.729515032 Simplifying x = 121.729515032Subproblem 2
x + -77.5 = -44.229515032 Simplifying x + -77.5 = -44.229515032 Reorder the terms: -77.5 + x = -44.229515032 Solving -77.5 + x = -44.229515032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '77.5' to each side of the equation. -77.5 + 77.5 + x = -44.229515032 + 77.5 Combine like terms: -77.5 + 77.5 = 0.0 0.0 + x = -44.229515032 + 77.5 x = -44.229515032 + 77.5 Combine like terms: -44.229515032 + 77.5 = 33.270484968 x = 33.270484968 Simplifying x = 33.270484968Solution
The solution to the problem is based on the solutions from the subproblems. x = {121.729515032, 33.270484968}Solution
x = {121.729515032, 33.270484968}
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