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Simplifying 7x3 + 8x2 + 33x = 0 Reorder the terms: 33x + 8x2 + 7x3 = 0 Solving 33x + 8x2 + 7x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(33 + 8x + 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 '(33 + 8x + 7x2)' equal to zero and attempt to solve: Simplifying 33 + 8x + 7x2 = 0 Solving 33 + 8x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 4.714285714 + 1.142857143x + x2 = 0 Move the constant term to the right: Add '-4.714285714' to each side of the equation. 4.714285714 + 1.142857143x + -4.714285714 + x2 = 0 + -4.714285714 Reorder the terms: 4.714285714 + -4.714285714 + 1.142857143x + x2 = 0 + -4.714285714 Combine like terms: 4.714285714 + -4.714285714 = 0.000000000 0.000000000 + 1.142857143x + x2 = 0 + -4.714285714 1.142857143x + x2 = 0 + -4.714285714 Combine like terms: 0 + -4.714285714 = -4.714285714 1.142857143x + x2 = -4.714285714 The x term is 1.142857143x. Take half its coefficient (0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. 1.142857143x + 0.3265306123 + x2 = -4.714285714 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143x + x2 = -4.714285714 + 0.3265306123 Combine like terms: -4.714285714 + 0.3265306123 = -4.3877551017 0.3265306123 + 1.142857143x + x2 = -4.3877551017 Factor a perfect square on the left side: (x + 0.5714285715)(x + 0.5714285715) = -4.3877551017 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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