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Simplifying 12x3 + 8x2 + -51x = 0 Reorder the terms: -51x + 8x2 + 12x3 = 0 Solving -51x + 8x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-51 + 8x + 12x2) = 0Subproblem 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 '(-51 + 8x + 12x2)' equal to zero and attempt to solve: Simplifying -51 + 8x + 12x2 = 0 Solving -51 + 8x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -4.25 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + 0.6666666667x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + 0.6666666667x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + 0.6666666667x + x2 = 0 + 4.25 0.6666666667x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 0.6666666667x + x2 = 4.25 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 4.25 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 4.25 + 0.1111111112 Combine like terms: 4.25 + 0.1111111112 = 4.3611111112 0.1111111112 + 0.6666666667x + x2 = 4.3611111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 4.3611111112 Calculate the square root of the right side: 2.088327348 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 2.088327348 and -2.088327348.Subproblem 1
x + 0.3333333334 = 2.088327348 Simplifying x + 0.3333333334 = 2.088327348 Reorder the terms: 0.3333333334 + x = 2.088327348 Solving 0.3333333334 + x = 2.088327348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 2.088327348 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 2.088327348 + -0.3333333334 x = 2.088327348 + -0.3333333334 Combine like terms: 2.088327348 + -0.3333333334 = 1.7549940146 x = 1.7549940146 Simplifying x = 1.7549940146Subproblem 2
x + 0.3333333334 = -2.088327348 Simplifying x + 0.3333333334 = -2.088327348 Reorder the terms: 0.3333333334 + x = -2.088327348 Solving 0.3333333334 + x = -2.088327348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -2.088327348 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -2.088327348 + -0.3333333334 x = -2.088327348 + -0.3333333334 Combine like terms: -2.088327348 + -0.3333333334 = -2.4216606814 x = -2.4216606814 Simplifying x = -2.4216606814Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7549940146, -2.4216606814}Solution
x = {0, 1.7549940146, -2.4216606814}
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