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Simplifying 2x2 + 4x = 250 Reorder the terms: 4x + 2x2 = 250 Solving 4x + 2x2 = 250 Solving for variable 'x'. Reorder the terms: -250 + 4x + 2x2 = 250 + -250 Combine like terms: 250 + -250 = 0 -250 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-125 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-125 + 2x + x2)' equal to zero and attempt to solve: Simplifying -125 + 2x + x2 = 0 Solving -125 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + 2x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + 2x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 2x + x2 = 0 + 125 2x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 2x + x2 = 125 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 = 125 + 1 Reorder the terms: 1 + 2x + x2 = 125 + 1 Combine like terms: 125 + 1 = 126 1 + 2x + x2 = 126 Factor a perfect square on the left side: (x + 1)(x + 1) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (x + 1) equal to 11.22497216 and -11.22497216.Subproblem 1
x + 1 = 11.22497216 Simplifying x + 1 = 11.22497216 Reorder the terms: 1 + x = 11.22497216 Solving 1 + x = 11.22497216 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 = 11.22497216 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.22497216 + -1 x = 11.22497216 + -1 Combine like terms: 11.22497216 + -1 = 10.22497216 x = 10.22497216 Simplifying x = 10.22497216Subproblem 2
x + 1 = -11.22497216 Simplifying x + 1 = -11.22497216 Reorder the terms: 1 + x = -11.22497216 Solving 1 + x = -11.22497216 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 = -11.22497216 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.22497216 + -1 x = -11.22497216 + -1 Combine like terms: -11.22497216 + -1 = -12.22497216 x = -12.22497216 Simplifying x = -12.22497216Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.22497216, -12.22497216}Solution
x = {10.22497216, -12.22497216}
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