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Simplifying 2x2 + 4x + 4 = 240 Reorder the terms: 4 + 4x + 2x2 = 240 Solving 4 + 4x + 2x2 = 240 Solving for variable 'x'. Reorder the terms: 4 + -240 + 4x + 2x2 = 240 + -240 Combine like terms: 4 + -240 = -236 -236 + 4x + 2x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -236 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-118 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-118 + 2x + x2)' equal to zero and attempt to solve: Simplifying -118 + 2x + x2 = 0 Solving -118 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '118' to each side of the equation. -118 + 2x + 118 + x2 = 0 + 118 Reorder the terms: -118 + 118 + 2x + x2 = 0 + 118 Combine like terms: -118 + 118 = 0 0 + 2x + x2 = 0 + 118 2x + x2 = 0 + 118 Combine like terms: 0 + 118 = 118 2x + x2 = 118 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 118 + 1 Reorder the terms: 1 + 2x + x2 = 118 + 1 Combine like terms: 118 + 1 = 119 1 + 2x + x2 = 119 Factor a perfect square on the left side: (x + 1)(x + 1) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (x + 1) equal to 10.908712115 and -10.908712115.Subproblem 1
x + 1 = 10.908712115 Simplifying x + 1 = 10.908712115 Reorder the terms: 1 + x = 10.908712115 Solving 1 + x = 10.908712115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 10.908712115 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.908712115 + -1 x = 10.908712115 + -1 Combine like terms: 10.908712115 + -1 = 9.908712115 x = 9.908712115 Simplifying x = 9.908712115Subproblem 2
x + 1 = -10.908712115 Simplifying x + 1 = -10.908712115 Reorder the terms: 1 + x = -10.908712115 Solving 1 + x = -10.908712115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -10.908712115 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.908712115 + -1 x = -10.908712115 + -1 Combine like terms: -10.908712115 + -1 = -11.908712115 x = -11.908712115 Simplifying x = -11.908712115Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.908712115, -11.908712115}Solution
x = {9.908712115, -11.908712115}
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