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Simplifying 2x2 + 240x + -1800 = 0 Reorder the terms: -1800 + 240x + 2x2 = 0 Solving -1800 + 240x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-900 + 120x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-900 + 120x + x2)' equal to zero and attempt to solve: Simplifying -900 + 120x + x2 = 0 Solving -900 + 120x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '900' to each side of the equation. -900 + 120x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + 120x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 120x + x2 = 0 + 900 120x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 120x + x2 = 900 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 = 900 + 3600 Reorder the terms: 3600 + 120x + x2 = 900 + 3600 Combine like terms: 900 + 3600 = 4500 3600 + 120x + x2 = 4500 Factor a perfect square on the left side: (x + 60)(x + 60) = 4500 Calculate the square root of the right side: 67.082039325 Break this problem into two subproblems by setting (x + 60) equal to 67.082039325 and -67.082039325.Subproblem 1
x + 60 = 67.082039325 Simplifying x + 60 = 67.082039325 Reorder the terms: 60 + x = 67.082039325 Solving 60 + x = 67.082039325 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 = 67.082039325 + -60 Combine like terms: 60 + -60 = 0 0 + x = 67.082039325 + -60 x = 67.082039325 + -60 Combine like terms: 67.082039325 + -60 = 7.082039325 x = 7.082039325 Simplifying x = 7.082039325Subproblem 2
x + 60 = -67.082039325 Simplifying x + 60 = -67.082039325 Reorder the terms: 60 + x = -67.082039325 Solving 60 + x = -67.082039325 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 = -67.082039325 + -60 Combine like terms: 60 + -60 = 0 0 + x = -67.082039325 + -60 x = -67.082039325 + -60 Combine like terms: -67.082039325 + -60 = -127.082039325 x = -127.082039325 Simplifying x = -127.082039325Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.082039325, -127.082039325}Solution
x = {7.082039325, -127.082039325}
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