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Simplifying 12x3 + 68x2 + 84x = 0 Reorder the terms: 84x + 68x2 + 12x3 = 0 Solving 84x + 68x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(21 + 17x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(21 + 17x + 3x2)' equal to zero and attempt to solve: Simplifying 21 + 17x + 3x2 = 0 Solving 21 + 17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 5.666666667x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 5.666666667x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5.666666667x + x2 = 0 + -7 5.666666667x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 5.666666667x + x2 = -7 The x term is 5.666666667x. Take half its coefficient (2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. 5.666666667x + 8.027777782 + x2 = -7 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = -7 + 8.027777782 Combine like terms: -7 + 8.027777782 = 1.027777782 8.027777782 + 5.666666667x + x2 = 1.027777782 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 1.027777782 Calculate the square root of the right side: 1.013793757 Break this problem into two subproblems by setting (x + 2.833333334) equal to 1.013793757 and -1.013793757.Subproblem 1
x + 2.833333334 = 1.013793757 Simplifying x + 2.833333334 = 1.013793757 Reorder the terms: 2.833333334 + x = 1.013793757 Solving 2.833333334 + x = 1.013793757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = 1.013793757 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 1.013793757 + -2.833333334 x = 1.013793757 + -2.833333334 Combine like terms: 1.013793757 + -2.833333334 = -1.819539577 x = -1.819539577 Simplifying x = -1.819539577Subproblem 2
x + 2.833333334 = -1.013793757 Simplifying x + 2.833333334 = -1.013793757 Reorder the terms: 2.833333334 + x = -1.013793757 Solving 2.833333334 + x = -1.013793757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = -1.013793757 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -1.013793757 + -2.833333334 x = -1.013793757 + -2.833333334 Combine like terms: -1.013793757 + -2.833333334 = -3.847127091 x = -3.847127091 Simplifying x = -3.847127091Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.819539577, -3.847127091}Solution
x = {0, -1.819539577, -3.847127091}
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