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Simplifying 14x3 + -18x2 + -15x = 0 Reorder the terms: -15x + -18x2 + 14x3 = 0 Solving -15x + -18x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-15 + -18x + 14x2) = 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 + -18x + 14x2)' equal to zero and attempt to solve: Simplifying -15 + -18x + 14x2 = 0 Solving -15 + -18x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.071428571 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '1.071428571' to each side of the equation. -1.071428571 + -1.285714286x + 1.071428571 + x2 = 0 + 1.071428571 Reorder the terms: -1.071428571 + 1.071428571 + -1.285714286x + x2 = 0 + 1.071428571 Combine like terms: -1.071428571 + 1.071428571 = 0.000000000 0.000000000 + -1.285714286x + x2 = 0 + 1.071428571 -1.285714286x + x2 = 0 + 1.071428571 Combine like terms: 0 + 1.071428571 = 1.071428571 -1.285714286x + x2 = 1.071428571 The x term is -1.285714286x. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286x + 0.4132653063 + x2 = 1.071428571 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = 1.071428571 + 0.4132653063 Combine like terms: 1.071428571 + 0.4132653063 = 1.4846938773 0.4132653063 + -1.285714286x + x2 = 1.4846938773 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = 1.4846938773 Calculate the square root of the right side: 1.218480151 Break this problem into two subproblems by setting (x + -0.642857143) equal to 1.218480151 and -1.218480151.Subproblem 1
x + -0.642857143 = 1.218480151 Simplifying x + -0.642857143 = 1.218480151 Reorder the terms: -0.642857143 + x = 1.218480151 Solving -0.642857143 + x = 1.218480151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + x = 1.218480151 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = 1.218480151 + 0.642857143 x = 1.218480151 + 0.642857143 Combine like terms: 1.218480151 + 0.642857143 = 1.861337294 x = 1.861337294 Simplifying x = 1.861337294Subproblem 2
x + -0.642857143 = -1.218480151 Simplifying x + -0.642857143 = -1.218480151 Reorder the terms: -0.642857143 + x = -1.218480151 Solving -0.642857143 + x = -1.218480151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + x = -1.218480151 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = -1.218480151 + 0.642857143 x = -1.218480151 + 0.642857143 Combine like terms: -1.218480151 + 0.642857143 = -0.575623008 x = -0.575623008 Simplifying x = -0.575623008Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.861337294, -0.575623008}Solution
x = {0, 1.861337294, -0.575623008}
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