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Simplifying 0 = x2 + 240x + 3600 Reorder the terms: 0 = 3600 + 240x + x2 Solving 0 = 3600 + 240x + x2 Solving for variable 'x'. Combine like terms: 0 + -3600 = -3600 -3600 + -240x + -1x2 = 3600 + 240x + x2 + -3600 + -240x + -1x2 Reorder the terms: -3600 + -240x + -1x2 = 3600 + -3600 + 240x + -240x + x2 + -1x2 Combine like terms: 3600 + -3600 = 0 -3600 + -240x + -1x2 = 0 + 240x + -240x + x2 + -1x2 -3600 + -240x + -1x2 = 240x + -240x + x2 + -1x2 Combine like terms: 240x + -240x = 0 -3600 + -240x + -1x2 = 0 + x2 + -1x2 -3600 + -240x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -3600 + -240x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3600 + 240x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3600 + 240x + x2)' equal to zero and attempt to solve: Simplifying 3600 + 240x + x2 = 0 Solving 3600 + 240x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3600' to each side of the equation. 3600 + 240x + -3600 + x2 = 0 + -3600 Reorder the terms: 3600 + -3600 + 240x + x2 = 0 + -3600 Combine like terms: 3600 + -3600 = 0 0 + 240x + x2 = 0 + -3600 240x + x2 = 0 + -3600 Combine like terms: 0 + -3600 = -3600 240x + x2 = -3600 The x term is 240x. Take half its coefficient (120). Square it (14400) and add it to both sides. Add '14400' to each side of the equation. 240x + 14400 + x2 = -3600 + 14400 Reorder the terms: 14400 + 240x + x2 = -3600 + 14400 Combine like terms: -3600 + 14400 = 10800 14400 + 240x + x2 = 10800 Factor a perfect square on the left side: (x + 120)(x + 120) = 10800 Calculate the square root of the right side: 103.923048454 Break this problem into two subproblems by setting (x + 120) equal to 103.923048454 and -103.923048454.Subproblem 1
x + 120 = 103.923048454 Simplifying x + 120 = 103.923048454 Reorder the terms: 120 + x = 103.923048454 Solving 120 + x = 103.923048454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-120' to each side of the equation. 120 + -120 + x = 103.923048454 + -120 Combine like terms: 120 + -120 = 0 0 + x = 103.923048454 + -120 x = 103.923048454 + -120 Combine like terms: 103.923048454 + -120 = -16.076951546 x = -16.076951546 Simplifying x = -16.076951546Subproblem 2
x + 120 = -103.923048454 Simplifying x + 120 = -103.923048454 Reorder the terms: 120 + x = -103.923048454 Solving 120 + x = -103.923048454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-120' to each side of the equation. 120 + -120 + x = -103.923048454 + -120 Combine like terms: 120 + -120 = 0 0 + x = -103.923048454 + -120 x = -103.923048454 + -120 Combine like terms: -103.923048454 + -120 = -223.923048454 x = -223.923048454 Simplifying x = -223.923048454Solution
The solution to the problem is based on the solutions from the subproblems. x = {-16.076951546, -223.923048454}Solution
x = {-16.076951546, -223.923048454}
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