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Simplifying -15x3 + -6x2 + 20x = 0 Reorder the terms: 20x + -6x2 + -15x3 = 0 Solving 20x + -6x2 + -15x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(20 + -6x + -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 '(20 + -6x + -15x2)' equal to zero and attempt to solve: Simplifying 20 + -6x + -15x2 = 0 Solving 20 + -6x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -1.333333333 + 0.4x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 0.4x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 0.4x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 0.4x + x2 = 0 + 1.333333333 0.4x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 0.4x + x2 = 1.333333333 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 1.333333333 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 1.333333333 + 0.04 Combine like terms: 1.333333333 + 0.04 = 1.373333333 0.04 + 0.4x + x2 = 1.373333333 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 1.373333333 Calculate the square root of the right side: 1.171893055 Break this problem into two subproblems by setting (x + 0.2) equal to 1.171893055 and -1.171893055.Subproblem 1
x + 0.2 = 1.171893055 Simplifying x + 0.2 = 1.171893055 Reorder the terms: 0.2 + x = 1.171893055 Solving 0.2 + x = 1.171893055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 1.171893055 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1.171893055 + -0.2 x = 1.171893055 + -0.2 Combine like terms: 1.171893055 + -0.2 = 0.971893055 x = 0.971893055 Simplifying x = 0.971893055Subproblem 2
x + 0.2 = -1.171893055 Simplifying x + 0.2 = -1.171893055 Reorder the terms: 0.2 + x = -1.171893055 Solving 0.2 + x = -1.171893055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -1.171893055 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1.171893055 + -0.2 x = -1.171893055 + -0.2 Combine like terms: -1.171893055 + -0.2 = -1.371893055 x = -1.371893055 Simplifying x = -1.371893055Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.971893055, -1.371893055}Solution
x = {0, 0.971893055, -1.371893055}
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