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Simplifying 3x2 + -36x = 141 Reorder the terms: -36x + 3x2 = 141 Solving -36x + 3x2 = 141 Solving for variable 'x'. Reorder the terms: -141 + -36x + 3x2 = 141 + -141 Combine like terms: 141 + -141 = 0 -141 + -36x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-47 + -12x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-47 + -12x + x2)' equal to zero and attempt to solve: Simplifying -47 + -12x + x2 = 0 Solving -47 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -12x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + -12x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -12x + x2 = 0 + 47 -12x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 -12x + x2 = 47 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 47 + 36 Reorder the terms: 36 + -12x + x2 = 47 + 36 Combine like terms: 47 + 36 = 83 36 + -12x + x2 = 83 Factor a perfect square on the left side: (x + -6)(x + -6) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (x + -6) equal to 9.110433579 and -9.110433579.Subproblem 1
x + -6 = 9.110433579 Simplifying x + -6 = 9.110433579 Reorder the terms: -6 + x = 9.110433579 Solving -6 + x = 9.110433579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 9.110433579 + 6 Combine like terms: -6 + 6 = 0 0 + x = 9.110433579 + 6 x = 9.110433579 + 6 Combine like terms: 9.110433579 + 6 = 15.110433579 x = 15.110433579 Simplifying x = 15.110433579Subproblem 2
x + -6 = -9.110433579 Simplifying x + -6 = -9.110433579 Reorder the terms: -6 + x = -9.110433579 Solving -6 + x = -9.110433579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -9.110433579 + 6 Combine like terms: -6 + 6 = 0 0 + x = -9.110433579 + 6 x = -9.110433579 + 6 Combine like terms: -9.110433579 + 6 = -3.110433579 x = -3.110433579 Simplifying x = -3.110433579Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.110433579, -3.110433579}Solution
x = {15.110433579, -3.110433579}
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