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Simplifying 2x2 + -48x + 140 = -60 Reorder the terms: 140 + -48x + 2x2 = -60 Solving 140 + -48x + 2x2 = -60 Solving for variable 'x'. Reorder the terms: 140 + 60 + -48x + 2x2 = -60 + 60 Combine like terms: 140 + 60 = 200 200 + -48x + 2x2 = -60 + 60 Combine like terms: -60 + 60 = 0 200 + -48x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(100 + -24x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(100 + -24x + x2)' equal to zero and attempt to solve: Simplifying 100 + -24x + x2 = 0 Solving 100 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -24x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -24x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -24x + x2 = 0 + -100 -24x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -24x + x2 = -100 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 = -100 + 144 Reorder the terms: 144 + -24x + x2 = -100 + 144 Combine like terms: -100 + 144 = 44 144 + -24x + x2 = 44 Factor a perfect square on the left side: (x + -12)(x + -12) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + -12) equal to 6.633249581 and -6.633249581.Subproblem 1
x + -12 = 6.633249581 Simplifying x + -12 = 6.633249581 Reorder the terms: -12 + x = 6.633249581 Solving -12 + x = 6.633249581 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 = 6.633249581 + 12 Combine like terms: -12 + 12 = 0 0 + x = 6.633249581 + 12 x = 6.633249581 + 12 Combine like terms: 6.633249581 + 12 = 18.633249581 x = 18.633249581 Simplifying x = 18.633249581Subproblem 2
x + -12 = -6.633249581 Simplifying x + -12 = -6.633249581 Reorder the terms: -12 + x = -6.633249581 Solving -12 + x = -6.633249581 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 = -6.633249581 + 12 Combine like terms: -12 + 12 = 0 0 + x = -6.633249581 + 12 x = -6.633249581 + 12 Combine like terms: -6.633249581 + 12 = 5.366750419 x = 5.366750419 Simplifying x = 5.366750419Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.633249581, 5.366750419}Solution
x = {18.633249581, 5.366750419}
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