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Simplifying -2x2 + -36x = 110 Reorder the terms: -36x + -2x2 = 110 Solving -36x + -2x2 = 110 Solving for variable 'x'. Reorder the terms: -110 + -36x + -2x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + -36x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(55 + 18x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(55 + 18x + x2)' equal to zero and attempt to solve: Simplifying 55 + 18x + x2 = 0 Solving 55 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-55' to each side of the equation. 55 + 18x + -55 + x2 = 0 + -55 Reorder the terms: 55 + -55 + 18x + x2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + 18x + x2 = 0 + -55 18x + x2 = 0 + -55 Combine like terms: 0 + -55 = -55 18x + x2 = -55 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 = -55 + 81 Reorder the terms: 81 + 18x + x2 = -55 + 81 Combine like terms: -55 + 81 = 26 81 + 18x + x2 = 26 Factor a perfect square on the left side: (x + 9)(x + 9) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + 9) equal to 5.099019514 and -5.099019514.Subproblem 1
x + 9 = 5.099019514 Simplifying x + 9 = 5.099019514 Reorder the terms: 9 + x = 5.099019514 Solving 9 + x = 5.099019514 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 = 5.099019514 + -9 Combine like terms: 9 + -9 = 0 0 + x = 5.099019514 + -9 x = 5.099019514 + -9 Combine like terms: 5.099019514 + -9 = -3.900980486 x = -3.900980486 Simplifying x = -3.900980486Subproblem 2
x + 9 = -5.099019514 Simplifying x + 9 = -5.099019514 Reorder the terms: 9 + x = -5.099019514 Solving 9 + x = -5.099019514 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 = -5.099019514 + -9 Combine like terms: 9 + -9 = 0 0 + x = -5.099019514 + -9 x = -5.099019514 + -9 Combine like terms: -5.099019514 + -9 = -14.099019514 x = -14.099019514 Simplifying x = -14.099019514Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.900980486, -14.099019514}Solution
x = {-3.900980486, -14.099019514}
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