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Simplifying -35x5 + 35x4 + 15x3 = 0 Reorder the terms: 15x3 + 35x4 + -35x5 = 0 Solving 15x3 + 35x4 + -35x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x3'. 5x3(3 + 7x + -7x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(3 + 7x + -7x2)' equal to zero and attempt to solve: Simplifying 3 + 7x + -7x2 = 0 Solving 3 + 7x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.4285714286 + -1x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -1x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -1x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.4285714286 -1x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -1x + x2 = 0.4285714286 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.4285714286 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.4285714286 + 0.25 Combine like terms: 0.4285714286 + 0.25 = 0.6785714286 0.25 + -1x + x2 = 0.6785714286 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.6785714286 Calculate the square root of the right side: 0.823754471 Break this problem into two subproblems by setting (x + -0.5) equal to 0.823754471 and -0.823754471.Subproblem 1
x + -0.5 = 0.823754471 Simplifying x + -0.5 = 0.823754471 Reorder the terms: -0.5 + x = 0.823754471 Solving -0.5 + x = 0.823754471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.823754471 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.823754471 + 0.5 x = 0.823754471 + 0.5 Combine like terms: 0.823754471 + 0.5 = 1.323754471 x = 1.323754471 Simplifying x = 1.323754471Subproblem 2
x + -0.5 = -0.823754471 Simplifying x + -0.5 = -0.823754471 Reorder the terms: -0.5 + x = -0.823754471 Solving -0.5 + x = -0.823754471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.823754471 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.823754471 + 0.5 x = -0.823754471 + 0.5 Combine like terms: -0.823754471 + 0.5 = -0.323754471 x = -0.323754471 Simplifying x = -0.323754471Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.323754471, -0.323754471}Solution
x = {1.323754471, -0.323754471}
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