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Simplifying 3x3 + 14x2 + -12x = 0 Reorder the terms: -12x + 14x2 + 3x3 = 0 Solving -12x + 14x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-12 + 14x + 3x2) = 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 '(-12 + 14x + 3x2)' equal to zero and attempt to solve: Simplifying -12 + 14x + 3x2 = 0 Solving -12 + 14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 4.666666667x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 4.666666667x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4.666666667x + x2 = 0 + 4 4.666666667x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 4.666666667x + x2 = 4 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = 4 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 4 + 5.444444448 Combine like terms: 4 + 5.444444448 = 9.444444448 5.444444448 + 4.666666667x + x2 = 9.444444448 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 9.444444448 Calculate the square root of the right side: 3.073181486 Break this problem into two subproblems by setting (x + 2.333333334) equal to 3.073181486 and -3.073181486.Subproblem 1
x + 2.333333334 = 3.073181486 Simplifying x + 2.333333334 = 3.073181486 Reorder the terms: 2.333333334 + x = 3.073181486 Solving 2.333333334 + x = 3.073181486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 3.073181486 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 3.073181486 + -2.333333334 x = 3.073181486 + -2.333333334 Combine like terms: 3.073181486 + -2.333333334 = 0.739848152 x = 0.739848152 Simplifying x = 0.739848152Subproblem 2
x + 2.333333334 = -3.073181486 Simplifying x + 2.333333334 = -3.073181486 Reorder the terms: 2.333333334 + x = -3.073181486 Solving 2.333333334 + x = -3.073181486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -3.073181486 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -3.073181486 + -2.333333334 x = -3.073181486 + -2.333333334 Combine like terms: -3.073181486 + -2.333333334 = -5.40651482 x = -5.40651482 Simplifying x = -5.40651482Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.739848152, -5.40651482}Solution
x = {0, 0.739848152, -5.40651482}
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