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Simplifying 3x3 + 5x2 + -57x = 0 Reorder the terms: -57x + 5x2 + 3x3 = 0 Solving -57x + 5x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-57 + 5x + 3x2) = 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 '(-57 + 5x + 3x2)' equal to zero and attempt to solve: Simplifying -57 + 5x + 3x2 = 0 Solving -57 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -19 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + 1.666666667x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 1.666666667x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 1.666666667x + x2 = 0 + 19 1.666666667x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 1.666666667x + x2 = 19 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 19 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 19 + 0.6944444447 Combine like terms: 19 + 0.6944444447 = 19.6944444447 0.6944444447 + 1.666666667x + x2 = 19.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 19.6944444447 Calculate the square root of the right side: 4.437842319 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 4.437842319 and -4.437842319.Subproblem 1
x + 0.8333333335 = 4.437842319 Simplifying x + 0.8333333335 = 4.437842319 Reorder the terms: 0.8333333335 + x = 4.437842319 Solving 0.8333333335 + x = 4.437842319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 4.437842319 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 4.437842319 + -0.8333333335 x = 4.437842319 + -0.8333333335 Combine like terms: 4.437842319 + -0.8333333335 = 3.6045089855 x = 3.6045089855 Simplifying x = 3.6045089855Subproblem 2
x + 0.8333333335 = -4.437842319 Simplifying x + 0.8333333335 = -4.437842319 Reorder the terms: 0.8333333335 + x = -4.437842319 Solving 0.8333333335 + x = -4.437842319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -4.437842319 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -4.437842319 + -0.8333333335 x = -4.437842319 + -0.8333333335 Combine like terms: -4.437842319 + -0.8333333335 = -5.2711756525 x = -5.2711756525 Simplifying x = -5.2711756525Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6045089855, -5.2711756525}Solution
x = {0, 3.6045089855, -5.2711756525}
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