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Simplifying (15x3 + -19x2 + -4x) = 0 Reorder the terms: (-4x + -19x2 + 15x3) = 0 Remove parenthesis around (-4x + -19x2 + 15x3) -4x + -19x2 + 15x3 = 0 Solving -4x + -19x2 + 15x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + -19x + 15x2) = 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 + -19x + 15x2)' equal to zero and attempt to solve: Simplifying -4 + -19x + 15x2 = 0 Solving -4 + -19x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.2666666667 + -1.266666667x + x2 = 0 Move the constant term to the right: Add '0.2666666667' to each side of the equation. -0.2666666667 + -1.266666667x + 0.2666666667 + x2 = 0 + 0.2666666667 Reorder the terms: -0.2666666667 + 0.2666666667 + -1.266666667x + x2 = 0 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + -1.266666667x + x2 = 0 + 0.2666666667 -1.266666667x + x2 = 0 + 0.2666666667 Combine like terms: 0 + 0.2666666667 = 0.2666666667 -1.266666667x + x2 = 0.2666666667 The x term is -1.266666667x. Take half its coefficient (-0.6333333335). Square it (0.4011111113) and add it to both sides. Add '0.4011111113' to each side of the equation. -1.266666667x + 0.4011111113 + x2 = 0.2666666667 + 0.4011111113 Reorder the terms: 0.4011111113 + -1.266666667x + x2 = 0.2666666667 + 0.4011111113 Combine like terms: 0.2666666667 + 0.4011111113 = 0.667777778 0.4011111113 + -1.266666667x + x2 = 0.667777778 Factor a perfect square on the left side: (x + -0.6333333335)(x + -0.6333333335) = 0.667777778 Calculate the square root of the right side: 0.817176712 Break this problem into two subproblems by setting (x + -0.6333333335) equal to 0.817176712 and -0.817176712.Subproblem 1
x + -0.6333333335 = 0.817176712 Simplifying x + -0.6333333335 = 0.817176712 Reorder the terms: -0.6333333335 + x = 0.817176712 Solving -0.6333333335 + x = 0.817176712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6333333335' to each side of the equation. -0.6333333335 + 0.6333333335 + x = 0.817176712 + 0.6333333335 Combine like terms: -0.6333333335 + 0.6333333335 = 0.0000000000 0.0000000000 + x = 0.817176712 + 0.6333333335 x = 0.817176712 + 0.6333333335 Combine like terms: 0.817176712 + 0.6333333335 = 1.4505100455 x = 1.4505100455 Simplifying x = 1.4505100455Subproblem 2
x + -0.6333333335 = -0.817176712 Simplifying x + -0.6333333335 = -0.817176712 Reorder the terms: -0.6333333335 + x = -0.817176712 Solving -0.6333333335 + x = -0.817176712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6333333335' to each side of the equation. -0.6333333335 + 0.6333333335 + x = -0.817176712 + 0.6333333335 Combine like terms: -0.6333333335 + 0.6333333335 = 0.0000000000 0.0000000000 + x = -0.817176712 + 0.6333333335 x = -0.817176712 + 0.6333333335 Combine like terms: -0.817176712 + 0.6333333335 = -0.1838433785 x = -0.1838433785 Simplifying x = -0.1838433785Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4505100455, -0.1838433785}Solution
x = {0, 1.4505100455, -0.1838433785}
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