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Simplifying 340x + -2x2 = 100x + 4200 Reorder the terms: 340x + -2x2 = 4200 + 100x Solving 340x + -2x2 = 4200 + 100x Solving for variable 'x'. Reorder the terms: -4200 + 340x + -100x + -2x2 = 4200 + 100x + -4200 + -100x Combine like terms: 340x + -100x = 240x -4200 + 240x + -2x2 = 4200 + 100x + -4200 + -100x Reorder the terms: -4200 + 240x + -2x2 = 4200 + -4200 + 100x + -100x Combine like terms: 4200 + -4200 = 0 -4200 + 240x + -2x2 = 0 + 100x + -100x -4200 + 240x + -2x2 = 100x + -100x Combine like terms: 100x + -100x = 0 -4200 + 240x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2100 + 120x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2100 + 120x + -1x2)' equal to zero and attempt to solve: Simplifying -2100 + 120x + -1x2 = 0 Solving -2100 + 120x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2100 + -120x + x2 = 0 Move the constant term to the right: Add '-2100' to each side of the equation. 2100 + -120x + -2100 + x2 = 0 + -2100 Reorder the terms: 2100 + -2100 + -120x + x2 = 0 + -2100 Combine like terms: 2100 + -2100 = 0 0 + -120x + x2 = 0 + -2100 -120x + x2 = 0 + -2100 Combine like terms: 0 + -2100 = -2100 -120x + x2 = -2100 The x term is -120x. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120x + 3600 + x2 = -2100 + 3600 Reorder the terms: 3600 + -120x + x2 = -2100 + 3600 Combine like terms: -2100 + 3600 = 1500 3600 + -120x + x2 = 1500 Factor a perfect square on the left side: (x + -60)(x + -60) = 1500 Calculate the square root of the right side: 38.729833462 Break this problem into two subproblems by setting (x + -60) equal to 38.729833462 and -38.729833462.Subproblem 1
x + -60 = 38.729833462 Simplifying x + -60 = 38.729833462 Reorder the terms: -60 + x = 38.729833462 Solving -60 + x = 38.729833462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 38.729833462 + 60 Combine like terms: -60 + 60 = 0 0 + x = 38.729833462 + 60 x = 38.729833462 + 60 Combine like terms: 38.729833462 + 60 = 98.729833462 x = 98.729833462 Simplifying x = 98.729833462Subproblem 2
x + -60 = -38.729833462 Simplifying x + -60 = -38.729833462 Reorder the terms: -60 + x = -38.729833462 Solving -60 + x = -38.729833462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = -38.729833462 + 60 Combine like terms: -60 + 60 = 0 0 + x = -38.729833462 + 60 x = -38.729833462 + 60 Combine like terms: -38.729833462 + 60 = 21.270166538 x = 21.270166538 Simplifying x = 21.270166538Solution
The solution to the problem is based on the solutions from the subproblems. x = {98.729833462, 21.270166538}Solution
x = {98.729833462, 21.270166538}
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