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Simplifying 0 = 12x3 + -15x2 + -4x Reorder the terms: 0 = -4x + -15x2 + 12x3 Solving 0 = -4x + -15x2 + 12x3 Solving for variable 'x'. Remove the zero: 4x + 15x2 + -12x3 = -4x + -15x2 + 12x3 + 4x + 15x2 + -12x3 Reorder the terms: 4x + 15x2 + -12x3 = -4x + 4x + -15x2 + 15x2 + 12x3 + -12x3 Combine like terms: -4x + 4x = 0 4x + 15x2 + -12x3 = 0 + -15x2 + 15x2 + 12x3 + -12x3 4x + 15x2 + -12x3 = -15x2 + 15x2 + 12x3 + -12x3 Combine like terms: -15x2 + 15x2 = 0 4x + 15x2 + -12x3 = 0 + 12x3 + -12x3 4x + 15x2 + -12x3 = 12x3 + -12x3 Combine like terms: 12x3 + -12x3 = 0 4x + 15x2 + -12x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(4 + 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 '(4 + 15x + -12x2)' equal to zero and attempt to solve: Simplifying 4 + 15x + -12x2 = 0 Solving 4 + 15x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.3333333333 + -1.25x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -1.25x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -1.25x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -1.25x + x2 = 0 + 0.3333333333 -1.25x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -1.25x + x2 = 0.3333333333 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 = 0.3333333333 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 0.3333333333 + 0.390625 Combine like terms: 0.3333333333 + 0.390625 = 0.7239583333 0.390625 + -1.25x + x2 = 0.7239583333 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.7239583333 Calculate the square root of the right side: 0.850857411 Break this problem into two subproblems by setting (x + -0.625) equal to 0.850857411 and -0.850857411.Subproblem 1
x + -0.625 = 0.850857411 Simplifying x + -0.625 = 0.850857411 Reorder the terms: -0.625 + x = 0.850857411 Solving -0.625 + x = 0.850857411 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 = 0.850857411 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.850857411 + 0.625 x = 0.850857411 + 0.625 Combine like terms: 0.850857411 + 0.625 = 1.475857411 x = 1.475857411 Simplifying x = 1.475857411Subproblem 2
x + -0.625 = -0.850857411 Simplifying x + -0.625 = -0.850857411 Reorder the terms: -0.625 + x = -0.850857411 Solving -0.625 + x = -0.850857411 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 = -0.850857411 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.850857411 + 0.625 x = -0.850857411 + 0.625 Combine like terms: -0.850857411 + 0.625 = -0.225857411 x = -0.225857411 Simplifying x = -0.225857411Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.475857411, -0.225857411}Solution
x = {0, 1.475857411, -0.225857411}
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