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Simplifying 5x2 + -10x3 + -35x4 = 0 Solving 5x2 + -10x3 + -35x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x2'. 5x2(1 + -2x + -7x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(1 + -2x + -7x2)' equal to zero and attempt to solve: Simplifying 1 + -2x + -7x2 = 0 Solving 1 + -2x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.1428571429 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.2857142857x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 0.2857142857x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 0.2857142857x + x2 = 0 + 0.1428571429 0.2857142857x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 0.2857142857x + x2 = 0.1428571429 The x term is 0.2857142857x. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857x + 0.02040816328 + x2 = 0.1428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 0.1428571429 + 0.02040816328 Combine like terms: 0.1428571429 + 0.02040816328 = 0.16326530618 0.02040816328 + 0.2857142857x + x2 = 0.16326530618 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 0.16326530618 Calculate the square root of the right side: 0.404061018 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 0.404061018 and -0.404061018.Subproblem 1
x + 0.1428571429 = 0.404061018 Simplifying x + 0.1428571429 = 0.404061018 Reorder the terms: 0.1428571429 + x = 0.404061018 Solving 0.1428571429 + x = 0.404061018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = 0.404061018 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 0.404061018 + -0.1428571429 x = 0.404061018 + -0.1428571429 Combine like terms: 0.404061018 + -0.1428571429 = 0.2612038751 x = 0.2612038751 Simplifying x = 0.2612038751Subproblem 2
x + 0.1428571429 = -0.404061018 Simplifying x + 0.1428571429 = -0.404061018 Reorder the terms: 0.1428571429 + x = -0.404061018 Solving 0.1428571429 + x = -0.404061018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = -0.404061018 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -0.404061018 + -0.1428571429 x = -0.404061018 + -0.1428571429 Combine like terms: -0.404061018 + -0.1428571429 = -0.5469181609 x = -0.5469181609 Simplifying x = -0.5469181609Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2612038751, -0.5469181609}Solution
x = {0, 0.2612038751, -0.5469181609}
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