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Simplifying 2x2 + 4x + 6 = 180 Reorder the terms: 6 + 4x + 2x2 = 180 Solving 6 + 4x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: 6 + -180 + 4x + 2x2 = 180 + -180 Combine like terms: 6 + -180 = -174 -174 + 4x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -174 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-87 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-87 + 2x + x2)' equal to zero and attempt to solve: Simplifying -87 + 2x + x2 = 0 Solving -87 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '87' to each side of the equation. -87 + 2x + 87 + x2 = 0 + 87 Reorder the terms: -87 + 87 + 2x + x2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + 2x + x2 = 0 + 87 2x + x2 = 0 + 87 Combine like terms: 0 + 87 = 87 2x + x2 = 87 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 = 87 + 1 Reorder the terms: 1 + 2x + x2 = 87 + 1 Combine like terms: 87 + 1 = 88 1 + 2x + x2 = 88 Factor a perfect square on the left side: (x + 1)(x + 1) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x + 1) equal to 9.38083152 and -9.38083152.Subproblem 1
x + 1 = 9.38083152 Simplifying x + 1 = 9.38083152 Reorder the terms: 1 + x = 9.38083152 Solving 1 + x = 9.38083152 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 = 9.38083152 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.38083152 + -1 x = 9.38083152 + -1 Combine like terms: 9.38083152 + -1 = 8.38083152 x = 8.38083152 Simplifying x = 8.38083152Subproblem 2
x + 1 = -9.38083152 Simplifying x + 1 = -9.38083152 Reorder the terms: 1 + x = -9.38083152 Solving 1 + x = -9.38083152 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 = -9.38083152 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.38083152 + -1 x = -9.38083152 + -1 Combine like terms: -9.38083152 + -1 = -10.38083152 x = -10.38083152 Simplifying x = -10.38083152Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.38083152, -10.38083152}Solution
x = {8.38083152, -10.38083152}
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