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Simplifying 5x3 + 7x2 + 17x = 0 Reorder the terms: 17x + 7x2 + 5x3 = 0 Solving 17x + 7x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(17 + 7x + 5x2) = 0Subproblem 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 '(17 + 7x + 5x2)' equal to zero and attempt to solve: Simplifying 17 + 7x + 5x2 = 0 Solving 17 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.4 + 1.4x + x2 = 0 Move the constant term to the right: Add '-3.4' to each side of the equation. 3.4 + 1.4x + -3.4 + x2 = 0 + -3.4 Reorder the terms: 3.4 + -3.4 + 1.4x + x2 = 0 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + 1.4x + x2 = 0 + -3.4 1.4x + x2 = 0 + -3.4 Combine like terms: 0 + -3.4 = -3.4 1.4x + x2 = -3.4 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = -3.4 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = -3.4 + 0.49 Combine like terms: -3.4 + 0.49 = -2.91 0.49 + 1.4x + x2 = -2.91 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = -2.91 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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