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Simplifying 3x12 + 54x7 = 51x2 Reorder the terms: 54x7 + 3x12 = 51x2 Solving 54x7 + 3x12 = 51x2 Solving for variable 'x'. Reorder the terms: -51x2 + 54x7 + 3x12 = 51x2 + -51x2 Combine like terms: 51x2 + -51x2 = 0 -51x2 + 54x7 + 3x12 = 0 Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(-17 + 18x5 + x10) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-17 + 18x5 + x10)' equal to zero and attempt to solve: Simplifying -17 + 18x5 + x10 = 0 Solving -17 + 18x5 + x10 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 18x5 + 17 + x10 = 0 + 17 Reorder the terms: -17 + 17 + 18x5 + x10 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 18x5 + x10 = 0 + 17 18x5 + x10 = 0 + 17 Combine like terms: 0 + 17 = 17 18x5 + x10 = 17 The x term is 18x5. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x5 + 81 + x10 = 17 + 81 Reorder the terms: 81 + 18x5 + x10 = 17 + 81 Combine like terms: 17 + 81 = 98 81 + 18x5 + x10 = 98 Factor a perfect square on the left side: (x5 + 9)(x5 + 9) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x5 + 9) equal to 9.899494937 and -9.899494937.Subproblem 1
x5 + 9 = 9.899494937 Simplifying x5 + 9 = 9.899494937 Reorder the terms: 9 + x5 = 9.899494937 Solving 9 + x5 = 9.899494937 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 + x5 = 9.899494937 + -9 Combine like terms: 9 + -9 = 0 0 + x5 = 9.899494937 + -9 x5 = 9.899494937 + -9 Combine like terms: 9.899494937 + -9 = 0.899494937 x5 = 0.899494937 Simplifying x5 = 0.899494937 Reorder the terms: -0.899494937 + x5 = 0.899494937 + -0.899494937 Combine like terms: 0.899494937 + -0.899494937 = 0.000000000 -0.899494937 + x5 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x5 + 9 = -9.899494937 Simplifying x5 + 9 = -9.899494937 Reorder the terms: 9 + x5 = -9.899494937 Solving 9 + x5 = -9.899494937 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 + x5 = -9.899494937 + -9 Combine like terms: 9 + -9 = 0 0 + x5 = -9.899494937 + -9 x5 = -9.899494937 + -9 Combine like terms: -9.899494937 + -9 = -18.899494937 x5 = -18.899494937 Simplifying x5 = -18.899494937 Reorder the terms: 18.899494937 + x5 = -18.899494937 + 18.899494937 Combine like terms: -18.899494937 + 18.899494937 = 0.000000000 18.899494937 + x5 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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