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Simplifying 12x2 + 39x + -156 = 0 Reorder the terms: -156 + 39x + 12x2 = 0 Solving -156 + 39x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-52 + 13x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-52 + 13x + 4x2)' equal to zero and attempt to solve: Simplifying -52 + 13x + 4x2 = 0 Solving -52 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13 + 3.25x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 3.25x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 3.25x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 3.25x + x2 = 0 + 13 3.25x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 3.25x + x2 = 13 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = 13 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 13 + 2.640625 Combine like terms: 13 + 2.640625 = 15.640625 2.640625 + 3.25x + x2 = 15.640625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 15.640625 Calculate the square root of the right side: 3.954823005 Break this problem into two subproblems by setting (x + 1.625) equal to 3.954823005 and -3.954823005.Subproblem 1
x + 1.625 = 3.954823005 Simplifying x + 1.625 = 3.954823005 Reorder the terms: 1.625 + x = 3.954823005 Solving 1.625 + x = 3.954823005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 3.954823005 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 3.954823005 + -1.625 x = 3.954823005 + -1.625 Combine like terms: 3.954823005 + -1.625 = 2.329823005 x = 2.329823005 Simplifying x = 2.329823005Subproblem 2
x + 1.625 = -3.954823005 Simplifying x + 1.625 = -3.954823005 Reorder the terms: 1.625 + x = -3.954823005 Solving 1.625 + x = -3.954823005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -3.954823005 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -3.954823005 + -1.625 x = -3.954823005 + -1.625 Combine like terms: -3.954823005 + -1.625 = -5.579823005 x = -5.579823005 Simplifying x = -5.579823005Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.329823005, -5.579823005}Solution
x = {2.329823005, -5.579823005}
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