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Simplifying 2x2 + -36x = 112 + 0 Reorder the terms: -36x + 2x2 = 112 + 0 Combine like terms: 112 + 0 = 112 -36x + 2x2 = 112 Solving -36x + 2x2 = 112 Solving for variable 'x'. Reorder the terms: -112 + -36x + 2x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -112 + -36x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-56 + -18x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-56 + -18x + x2)' equal to zero and attempt to solve: Simplifying -56 + -18x + x2 = 0 Solving -56 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -18x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -18x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -18x + x2 = 0 + 56 -18x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -18x + x2 = 56 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 56 + 81 Reorder the terms: 81 + -18x + x2 = 56 + 81 Combine like terms: 56 + 81 = 137 81 + -18x + x2 = 137 Factor a perfect square on the left side: (x + -9)(x + -9) = 137 Calculate the square root of the right side: 11.704699911 Break this problem into two subproblems by setting (x + -9) equal to 11.704699911 and -11.704699911.Subproblem 1
x + -9 = 11.704699911 Simplifying x + -9 = 11.704699911 Reorder the terms: -9 + x = 11.704699911 Solving -9 + x = 11.704699911 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 11.704699911 + 9 Combine like terms: -9 + 9 = 0 0 + x = 11.704699911 + 9 x = 11.704699911 + 9 Combine like terms: 11.704699911 + 9 = 20.704699911 x = 20.704699911 Simplifying x = 20.704699911Subproblem 2
x + -9 = -11.704699911 Simplifying x + -9 = -11.704699911 Reorder the terms: -9 + x = -11.704699911 Solving -9 + x = -11.704699911 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -11.704699911 + 9 Combine like terms: -9 + 9 = 0 0 + x = -11.704699911 + 9 x = -11.704699911 + 9 Combine like terms: -11.704699911 + 9 = -2.704699911 x = -2.704699911 Simplifying x = -2.704699911Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.704699911, -2.704699911}Solution
x = {20.704699911, -2.704699911}
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