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Simplifying 12x3 + -15x2 + -19x = 0 Reorder the terms: -19x + -15x2 + 12x3 = 0 Solving -19x + -15x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-19 + -15x + 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 '(-19 + -15x + 12x2)' equal to zero and attempt to solve: Simplifying -19 + -15x + 12x2 = 0 Solving -19 + -15x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.583333333 + -1.25x + x2 = 0 Move the constant term to the right: Add '1.583333333' to each side of the equation. -1.583333333 + -1.25x + 1.583333333 + x2 = 0 + 1.583333333 Reorder the terms: -1.583333333 + 1.583333333 + -1.25x + x2 = 0 + 1.583333333 Combine like terms: -1.583333333 + 1.583333333 = 0.000000000 0.000000000 + -1.25x + x2 = 0 + 1.583333333 -1.25x + x2 = 0 + 1.583333333 Combine like terms: 0 + 1.583333333 = 1.583333333 -1.25x + x2 = 1.583333333 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 1.583333333 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 1.583333333 + 0.390625 Combine like terms: 1.583333333 + 0.390625 = 1.973958333 0.390625 + -1.25x + x2 = 1.973958333 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 1.973958333 Calculate the square root of the right side: 1.404976275 Break this problem into two subproblems by setting (x + -0.625) equal to 1.404976275 and -1.404976275.Subproblem 1
x + -0.625 = 1.404976275 Simplifying x + -0.625 = 1.404976275 Reorder the terms: -0.625 + x = 1.404976275 Solving -0.625 + x = 1.404976275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 1.404976275 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.404976275 + 0.625 x = 1.404976275 + 0.625 Combine like terms: 1.404976275 + 0.625 = 2.029976275 x = 2.029976275 Simplifying x = 2.029976275Subproblem 2
x + -0.625 = -1.404976275 Simplifying x + -0.625 = -1.404976275 Reorder the terms: -0.625 + x = -1.404976275 Solving -0.625 + x = -1.404976275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -1.404976275 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.404976275 + 0.625 x = -1.404976275 + 0.625 Combine like terms: -1.404976275 + 0.625 = -0.779976275 x = -0.779976275 Simplifying x = -0.779976275Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.029976275, -0.779976275}Solution
x = {0, 2.029976275, -0.779976275}
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