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Simplifying 3x(x + -12) = 51 Reorder the terms: 3x(-12 + x) = 51 (-12 * 3x + x * 3x) = 51 (-36x + 3x2) = 51 Solving -36x + 3x2 = 51 Solving for variable 'x'. Reorder the terms: -51 + -36x + 3x2 = 51 + -51 Combine like terms: 51 + -51 = 0 -51 + -36x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-17 + -12x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-17 + -12x + x2)' equal to zero and attempt to solve: Simplifying -17 + -12x + x2 = 0 Solving -17 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -12x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -12x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -12x + x2 = 0 + 17 -12x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -12x + x2 = 17 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 = 17 + 36 Reorder the terms: 36 + -12x + x2 = 17 + 36 Combine like terms: 17 + 36 = 53 36 + -12x + x2 = 53 Factor a perfect square on the left side: (x + -6)(x + -6) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + -6) equal to 7.280109889 and -7.280109889.Subproblem 1
x + -6 = 7.280109889 Simplifying x + -6 = 7.280109889 Reorder the terms: -6 + x = 7.280109889 Solving -6 + x = 7.280109889 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 = 7.280109889 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.280109889 + 6 x = 7.280109889 + 6 Combine like terms: 7.280109889 + 6 = 13.280109889 x = 13.280109889 Simplifying x = 13.280109889Subproblem 2
x + -6 = -7.280109889 Simplifying x + -6 = -7.280109889 Reorder the terms: -6 + x = -7.280109889 Solving -6 + x = -7.280109889 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 = -7.280109889 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.280109889 + 6 x = -7.280109889 + 6 Combine like terms: -7.280109889 + 6 = -1.280109889 x = -1.280109889 Simplifying x = -1.280109889Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.280109889, -1.280109889}Solution
x = {13.280109889, -1.280109889}
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