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Simplifying 7x4 + 5x3 + -1x2 = 0 Reorder the terms: -1x2 + 5x3 + 7x4 = 0 Solving -1x2 + 5x3 + 7x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-1 + 5x + 7x2) = 0Subproblem 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 + 5x + 7x2)' equal to zero and attempt to solve: Simplifying -1 + 5x + 7x2 = 0 Solving -1 + 5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.7142857143x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 0.7142857143x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 0.7142857143x + x2 = 0 + 0.1428571429 0.7142857143x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 0.7142857143x + x2 = 0.1428571429 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = 0.1428571429 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = 0.1428571429 + 0.1275510204 Combine like terms: 0.1428571429 + 0.1275510204 = 0.2704081633 0.1275510204 + 0.7142857143x + x2 = 0.2704081633 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 0.2704081633 Calculate the square root of the right side: 0.520007849 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 0.520007849 and -0.520007849.Subproblem 1
x + 0.3571428572 = 0.520007849 Simplifying x + 0.3571428572 = 0.520007849 Reorder the terms: 0.3571428572 + x = 0.520007849 Solving 0.3571428572 + x = 0.520007849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 0.520007849 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 0.520007849 + -0.3571428572 x = 0.520007849 + -0.3571428572 Combine like terms: 0.520007849 + -0.3571428572 = 0.1628649918 x = 0.1628649918 Simplifying x = 0.1628649918Subproblem 2
x + 0.3571428572 = -0.520007849 Simplifying x + 0.3571428572 = -0.520007849 Reorder the terms: 0.3571428572 + x = -0.520007849 Solving 0.3571428572 + x = -0.520007849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -0.520007849 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -0.520007849 + -0.3571428572 x = -0.520007849 + -0.3571428572 Combine like terms: -0.520007849 + -0.3571428572 = -0.8771507062 x = -0.8771507062 Simplifying x = -0.8771507062Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1628649918, -0.8771507062}Solution
x = {0, 0.1628649918, -0.8771507062}
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