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Simplifying 2x2 + 36x + -108 = 90 Reorder the terms: -108 + 36x + 2x2 = 90 Solving -108 + 36x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: -108 + -90 + 36x + 2x2 = 90 + -90 Combine like terms: -108 + -90 = -198 -198 + 36x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -198 + 36x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-99 + 18x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-99 + 18x + x2)' equal to zero and attempt to solve: Simplifying -99 + 18x + x2 = 0 Solving -99 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + 18x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + 18x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 18x + x2 = 0 + 99 18x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 18x + x2 = 99 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 = 99 + 81 Reorder the terms: 81 + 18x + x2 = 99 + 81 Combine like terms: 99 + 81 = 180 81 + 18x + x2 = 180 Factor a perfect square on the left side: (x + 9)(x + 9) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + 9) equal to 13.416407865 and -13.416407865.Subproblem 1
x + 9 = 13.416407865 Simplifying x + 9 = 13.416407865 Reorder the terms: 9 + x = 13.416407865 Solving 9 + x = 13.416407865 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 = 13.416407865 + -9 Combine like terms: 9 + -9 = 0 0 + x = 13.416407865 + -9 x = 13.416407865 + -9 Combine like terms: 13.416407865 + -9 = 4.416407865 x = 4.416407865 Simplifying x = 4.416407865Subproblem 2
x + 9 = -13.416407865 Simplifying x + 9 = -13.416407865 Reorder the terms: 9 + x = -13.416407865 Solving 9 + x = -13.416407865 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 = -13.416407865 + -9 Combine like terms: 9 + -9 = 0 0 + x = -13.416407865 + -9 x = -13.416407865 + -9 Combine like terms: -13.416407865 + -9 = -22.416407865 x = -22.416407865 Simplifying x = -22.416407865Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.416407865, -22.416407865}Solution
x = {4.416407865, -22.416407865}
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