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Simplifying 7x3 + x + -4(5x2 + -4x) = 0 Reorder the terms: 7x3 + x + -4(-4x + 5x2) = 0 7x3 + x + (-4x * -4 + 5x2 * -4) = 0 7x3 + x + (16x + -20x2) = 0 Reorder the terms: x + 16x + -20x2 + 7x3 = 0 Combine like terms: x + 16x = 17x 17x + -20x2 + 7x3 = 0 Solving 17x + -20x2 + 7x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(17 + -20x + 7x2) = 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 + -20x + 7x2)' equal to zero and attempt to solve: Simplifying 17 + -20x + 7x2 = 0 Solving 17 + -20x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.428571429 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '-2.428571429' to each side of the equation. 2.428571429 + -2.857142857x + -2.428571429 + x2 = 0 + -2.428571429 Reorder the terms: 2.428571429 + -2.428571429 + -2.857142857x + x2 = 0 + -2.428571429 Combine like terms: 2.428571429 + -2.428571429 = 0.000000000 0.000000000 + -2.857142857x + x2 = 0 + -2.428571429 -2.857142857x + x2 = 0 + -2.428571429 Combine like terms: 0 + -2.428571429 = -2.428571429 -2.857142857x + x2 = -2.428571429 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = -2.428571429 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = -2.428571429 + 2.040816328 Combine like terms: -2.428571429 + 2.040816328 = -0.387755101 2.040816328 + -2.857142857x + x2 = -0.387755101 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = -0.387755101 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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