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Simplifying 14x3 + -18x2 + -16x = 0 Reorder the terms: -16x + -18x2 + 14x3 = 0 Solving -16x + -18x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-8 + -9x + 7x2) = 0 Ignore the factor 2.Subproblem 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 '(-8 + -9x + 7x2)' equal to zero and attempt to solve: Simplifying -8 + -9x + 7x2 = 0 Solving -8 + -9x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -1.285714286x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -1.285714286x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -1.285714286x + x2 = 0 + 1.142857143 -1.285714286x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -1.285714286x + x2 = 1.142857143 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 = 1.142857143 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = 1.142857143 + 0.4132653063 Combine like terms: 1.142857143 + 0.4132653063 = 1.5561224493 0.4132653063 + -1.285714286x + x2 = 1.5561224493 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = 1.5561224493 Calculate the square root of the right side: 1.247446371 Break this problem into two subproblems by setting (x + -0.642857143) equal to 1.247446371 and -1.247446371.Subproblem 1
x + -0.642857143 = 1.247446371 Simplifying x + -0.642857143 = 1.247446371 Reorder the terms: -0.642857143 + x = 1.247446371 Solving -0.642857143 + x = 1.247446371 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 = 1.247446371 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = 1.247446371 + 0.642857143 x = 1.247446371 + 0.642857143 Combine like terms: 1.247446371 + 0.642857143 = 1.890303514 x = 1.890303514 Simplifying x = 1.890303514Subproblem 2
x + -0.642857143 = -1.247446371 Simplifying x + -0.642857143 = -1.247446371 Reorder the terms: -0.642857143 + x = -1.247446371 Solving -0.642857143 + x = -1.247446371 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 = -1.247446371 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = -1.247446371 + 0.642857143 x = -1.247446371 + 0.642857143 Combine like terms: -1.247446371 + 0.642857143 = -0.604589228 x = -0.604589228 Simplifying x = -0.604589228Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.890303514, -0.604589228}Solution
x = {0, 1.890303514, -0.604589228}
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