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Simplifying 2x2 + -18x + -236 = 0 Reorder the terms: -236 + -18x + 2x2 = 0 Solving -236 + -18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-118 + -9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-118 + -9x + x2)' equal to zero and attempt to solve: Simplifying -118 + -9x + x2 = 0 Solving -118 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '118' to each side of the equation. -118 + -9x + 118 + x2 = 0 + 118 Reorder the terms: -118 + 118 + -9x + x2 = 0 + 118 Combine like terms: -118 + 118 = 0 0 + -9x + x2 = 0 + 118 -9x + x2 = 0 + 118 Combine like terms: 0 + 118 = 118 -9x + x2 = 118 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 118 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 118 + 20.25 Combine like terms: 118 + 20.25 = 138.25 20.25 + -9x + x2 = 138.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 138.25 Calculate the square root of the right side: 11.757976016 Break this problem into two subproblems by setting (x + -4.5) equal to 11.757976016 and -11.757976016.Subproblem 1
x + -4.5 = 11.757976016 Simplifying x + -4.5 = 11.757976016 Reorder the terms: -4.5 + x = 11.757976016 Solving -4.5 + x = 11.757976016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 11.757976016 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 11.757976016 + 4.5 x = 11.757976016 + 4.5 Combine like terms: 11.757976016 + 4.5 = 16.257976016 x = 16.257976016 Simplifying x = 16.257976016Subproblem 2
x + -4.5 = -11.757976016 Simplifying x + -4.5 = -11.757976016 Reorder the terms: -4.5 + x = -11.757976016 Solving -4.5 + x = -11.757976016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -11.757976016 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -11.757976016 + 4.5 x = -11.757976016 + 4.5 Combine like terms: -11.757976016 + 4.5 = -7.257976016 x = -7.257976016 Simplifying x = -7.257976016Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.257976016, -7.257976016}Solution
x = {16.257976016, -7.257976016}
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