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Simplifying 14x3 + -16x2 + -6x = 0 Reorder the terms: -6x + -16x2 + 14x3 = 0 Solving -6x + -16x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-3 + -8x + 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 '(-3 + -8x + 7x2)' equal to zero and attempt to solve: Simplifying -3 + -8x + 7x2 = 0 Solving -3 + -8x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -1.142857143x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -1.142857143x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -1.142857143x + x2 = 0 + 0.4285714286 -1.142857143x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -1.142857143x + x2 = 0.4285714286 The x term is -1.142857143x. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143x + 0.3265306123 + x2 = 0.4285714286 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 0.4285714286 + 0.3265306123 Combine like terms: 0.4285714286 + 0.3265306123 = 0.7551020409 0.3265306123 + -1.142857143x + x2 = 0.7551020409 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 0.7551020409 Calculate the square root of the right side: 0.868966076 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 0.868966076 and -0.868966076.Subproblem 1
x + -0.5714285715 = 0.868966076 Simplifying x + -0.5714285715 = 0.868966076 Reorder the terms: -0.5714285715 + x = 0.868966076 Solving -0.5714285715 + x = 0.868966076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = 0.868966076 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 0.868966076 + 0.5714285715 x = 0.868966076 + 0.5714285715 Combine like terms: 0.868966076 + 0.5714285715 = 1.4403946475 x = 1.4403946475 Simplifying x = 1.4403946475Subproblem 2
x + -0.5714285715 = -0.868966076 Simplifying x + -0.5714285715 = -0.868966076 Reorder the terms: -0.5714285715 + x = -0.868966076 Solving -0.5714285715 + x = -0.868966076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = -0.868966076 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -0.868966076 + 0.5714285715 x = -0.868966076 + 0.5714285715 Combine like terms: -0.868966076 + 0.5714285715 = -0.2975375045 x = -0.2975375045 Simplifying x = -0.2975375045Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4403946475, -0.2975375045}Solution
x = {0, 1.4403946475, -0.2975375045}
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