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Simplifying 2x2 + 48x + 160 = 364 Reorder the terms: 160 + 48x + 2x2 = 364 Solving 160 + 48x + 2x2 = 364 Solving for variable 'x'. Reorder the terms: 160 + -364 + 48x + 2x2 = 364 + -364 Combine like terms: 160 + -364 = -204 -204 + 48x + 2x2 = 364 + -364 Combine like terms: 364 + -364 = 0 -204 + 48x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-102 + 24x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-102 + 24x + x2)' equal to zero and attempt to solve: Simplifying -102 + 24x + x2 = 0 Solving -102 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '102' to each side of the equation. -102 + 24x + 102 + x2 = 0 + 102 Reorder the terms: -102 + 102 + 24x + x2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + 24x + x2 = 0 + 102 24x + x2 = 0 + 102 Combine like terms: 0 + 102 = 102 24x + x2 = 102 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 102 + 144 Reorder the terms: 144 + 24x + x2 = 102 + 144 Combine like terms: 102 + 144 = 246 144 + 24x + x2 = 246 Factor a perfect square on the left side: (x + 12)(x + 12) = 246 Calculate the square root of the right side: 15.684387141 Break this problem into two subproblems by setting (x + 12) equal to 15.684387141 and -15.684387141.Subproblem 1
x + 12 = 15.684387141 Simplifying x + 12 = 15.684387141 Reorder the terms: 12 + x = 15.684387141 Solving 12 + x = 15.684387141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 15.684387141 + -12 Combine like terms: 12 + -12 = 0 0 + x = 15.684387141 + -12 x = 15.684387141 + -12 Combine like terms: 15.684387141 + -12 = 3.684387141 x = 3.684387141 Simplifying x = 3.684387141Subproblem 2
x + 12 = -15.684387141 Simplifying x + 12 = -15.684387141 Reorder the terms: 12 + x = -15.684387141 Solving 12 + x = -15.684387141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -15.684387141 + -12 Combine like terms: 12 + -12 = 0 0 + x = -15.684387141 + -12 x = -15.684387141 + -12 Combine like terms: -15.684387141 + -12 = -27.684387141 x = -27.684387141 Simplifying x = -27.684387141Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.684387141, -27.684387141}Solution
x = {3.684387141, -27.684387141}
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