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Simplifying 12(3x2 + -59x + -72) = 0 Reorder the terms: 12(-72 + -59x + 3x2) = 0 (-72 * 12 + -59x * 12 + 3x2 * 12) = 0 (-864 + -708x + 36x2) = 0 Solving -864 + -708x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-72 + -59x + 3x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-72 + -59x + 3x2)' equal to zero and attempt to solve: Simplifying -72 + -59x + 3x2 = 0 Solving -72 + -59x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -24 + -19.66666667x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -19.66666667x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -19.66666667x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -19.66666667x + x2 = 0 + 24 -19.66666667x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -19.66666667x + x2 = 24 The x term is -19.66666667x. Take half its coefficient (-9.833333335). Square it (96.69444448) and add it to both sides. Add '96.69444448' to each side of the equation. -19.66666667x + 96.69444448 + x2 = 24 + 96.69444448 Reorder the terms: 96.69444448 + -19.66666667x + x2 = 24 + 96.69444448 Combine like terms: 24 + 96.69444448 = 120.69444448 96.69444448 + -19.66666667x + x2 = 120.69444448 Factor a perfect square on the left side: (x + -9.833333335)(x + -9.833333335) = 120.69444448 Calculate the square root of the right side: 10.986102333 Break this problem into two subproblems by setting (x + -9.833333335) equal to 10.986102333 and -10.986102333.Subproblem 1
x + -9.833333335 = 10.986102333 Simplifying x + -9.833333335 = 10.986102333 Reorder the terms: -9.833333335 + x = 10.986102333 Solving -9.833333335 + x = 10.986102333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.833333335' to each side of the equation. -9.833333335 + 9.833333335 + x = 10.986102333 + 9.833333335 Combine like terms: -9.833333335 + 9.833333335 = 0.000000000 0.000000000 + x = 10.986102333 + 9.833333335 x = 10.986102333 + 9.833333335 Combine like terms: 10.986102333 + 9.833333335 = 20.819435668 x = 20.819435668 Simplifying x = 20.819435668Subproblem 2
x + -9.833333335 = -10.986102333 Simplifying x + -9.833333335 = -10.986102333 Reorder the terms: -9.833333335 + x = -10.986102333 Solving -9.833333335 + x = -10.986102333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.833333335' to each side of the equation. -9.833333335 + 9.833333335 + x = -10.986102333 + 9.833333335 Combine like terms: -9.833333335 + 9.833333335 = 0.000000000 0.000000000 + x = -10.986102333 + 9.833333335 x = -10.986102333 + 9.833333335 Combine like terms: -10.986102333 + 9.833333335 = -1.152768998 x = -1.152768998 Simplifying x = -1.152768998Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.819435668, -1.152768998}Solution
x = {20.819435668, -1.152768998}
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