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Simplifying 14x3 + -40x2 + 10x = 0 Reorder the terms: 10x + -40x2 + 14x3 = 0 Solving 10x + -40x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(5 + -20x + 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 '(5 + -20x + 7x2)' equal to zero and attempt to solve: Simplifying 5 + -20x + 7x2 = 0 Solving 5 + -20x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.7142857143 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -2.857142857x + -0.7142857143 + x2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -2.857142857x + x2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -2.857142857x + x2 = 0 + -0.7142857143 -2.857142857x + x2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -2.857142857x + x2 = -0.7142857143 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = -0.7142857143 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = -0.7142857143 + 2.040816328 Combine like terms: -0.7142857143 + 2.040816328 = 1.3265306137 2.040816328 + -2.857142857x + x2 = 1.3265306137 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 1.3265306137 Calculate the square root of the right side: 1.151751108 Break this problem into two subproblems by setting (x + -1.428571429) equal to 1.151751108 and -1.151751108.Subproblem 1
x + -1.428571429 = 1.151751108 Simplifying x + -1.428571429 = 1.151751108 Reorder the terms: -1.428571429 + x = 1.151751108 Solving -1.428571429 + x = 1.151751108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 1.151751108 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 1.151751108 + 1.428571429 x = 1.151751108 + 1.428571429 Combine like terms: 1.151751108 + 1.428571429 = 2.580322537 x = 2.580322537 Simplifying x = 2.580322537Subproblem 2
x + -1.428571429 = -1.151751108 Simplifying x + -1.428571429 = -1.151751108 Reorder the terms: -1.428571429 + x = -1.151751108 Solving -1.428571429 + x = -1.151751108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -1.151751108 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -1.151751108 + 1.428571429 x = -1.151751108 + 1.428571429 Combine like terms: -1.151751108 + 1.428571429 = 0.276820321 x = 0.276820321 Simplifying x = 0.276820321Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.580322537, 0.276820321}Solution
x = {0, 2.580322537, 0.276820321}
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