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Simplifying 35x4 + 5x3 + 25x2 = 0 Reorder the terms: 25x2 + 5x3 + 35x4 = 0 Solving 25x2 + 5x3 + 35x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x2'. 5x2(5 + x + 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 '(5 + x + 7x2)' equal to zero and attempt to solve: Simplifying 5 + x + 7x2 = 0 Solving 5 + x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.7142857143 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + 0.1428571429x + -0.7142857143 + x2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + 0.1428571429x + x2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + 0.1428571429x + x2 = 0 + -0.7142857143 0.1428571429x + x2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 0.1428571429x + x2 = -0.7142857143 The x term is x. 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. 0.1428571429x + 0.25 + x2 = -0.7142857143 + 0.25 Reorder the terms: 0.25 + 0.1428571429x + x2 = -0.7142857143 + 0.25 Combine like terms: -0.7142857143 + 0.25 = -0.4642857143 0.25 + 0.1428571429x + x2 = -0.4642857143 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.4642857143 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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