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Simplifying -12x3 + -13x2 + 15x = 0 Reorder the terms: 15x + -13x2 + -12x3 = 0 Solving 15x + -13x2 + -12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(15 + -13x + -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 '(15 + -13x + -12x2)' equal to zero and attempt to solve: Simplifying 15 + -13x + -12x2 = 0 Solving 15 + -13x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -1.25 + 1.083333333x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 1.083333333x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 1.083333333x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 1.083333333x + x2 = 0 + 1.25 1.083333333x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 1.083333333x + x2 = 1.25 The x term is 1.083333333x. Take half its coefficient (0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. 1.083333333x + 0.2934027776 + x2 = 1.25 + 0.2934027776 Reorder the terms: 0.2934027776 + 1.083333333x + x2 = 1.25 + 0.2934027776 Combine like terms: 1.25 + 0.2934027776 = 1.5434027776 0.2934027776 + 1.083333333x + x2 = 1.5434027776 Factor a perfect square on the left side: (x + 0.5416666665)(x + 0.5416666665) = 1.5434027776 Calculate the square root of the right side: 1.242337626 Break this problem into two subproblems by setting (x + 0.5416666665) equal to 1.242337626 and -1.242337626.Subproblem 1
x + 0.5416666665 = 1.242337626 Simplifying x + 0.5416666665 = 1.242337626 Reorder the terms: 0.5416666665 + x = 1.242337626 Solving 0.5416666665 + x = 1.242337626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5416666665' to each side of the equation. 0.5416666665 + -0.5416666665 + x = 1.242337626 + -0.5416666665 Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000 0.0000000000 + x = 1.242337626 + -0.5416666665 x = 1.242337626 + -0.5416666665 Combine like terms: 1.242337626 + -0.5416666665 = 0.7006709595 x = 0.7006709595 Simplifying x = 0.7006709595Subproblem 2
x + 0.5416666665 = -1.242337626 Simplifying x + 0.5416666665 = -1.242337626 Reorder the terms: 0.5416666665 + x = -1.242337626 Solving 0.5416666665 + x = -1.242337626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5416666665' to each side of the equation. 0.5416666665 + -0.5416666665 + x = -1.242337626 + -0.5416666665 Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000 0.0000000000 + x = -1.242337626 + -0.5416666665 x = -1.242337626 + -0.5416666665 Combine like terms: -1.242337626 + -0.5416666665 = -1.7840042925 x = -1.7840042925 Simplifying x = -1.7840042925Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7006709595, -1.7840042925}Solution
x = {0, 0.7006709595, -1.7840042925}
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