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Simplifying 0 = 3x4 + -3x3 + -117x2 Reorder the terms: 0 = -117x2 + -3x3 + 3x4 Solving 0 = -117x2 + -3x3 + 3x4 Solving for variable 'x'. Remove the zero: 117x2 + 3x3 + -3x4 = -117x2 + -3x3 + 3x4 + 117x2 + 3x3 + -3x4 Reorder the terms: 117x2 + 3x3 + -3x4 = -117x2 + 117x2 + -3x3 + 3x3 + 3x4 + -3x4 Combine like terms: -117x2 + 117x2 = 0 117x2 + 3x3 + -3x4 = 0 + -3x3 + 3x3 + 3x4 + -3x4 117x2 + 3x3 + -3x4 = -3x3 + 3x3 + 3x4 + -3x4 Combine like terms: -3x3 + 3x3 = 0 117x2 + 3x3 + -3x4 = 0 + 3x4 + -3x4 117x2 + 3x3 + -3x4 = 3x4 + -3x4 Combine like terms: 3x4 + -3x4 = 0 117x2 + 3x3 + -3x4 = 0 Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(39 + x + -1x2) = 0 Ignore the factor 3.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 '(39 + x + -1x2)' equal to zero and attempt to solve: Simplifying 39 + x + -1x2 = 0 Solving 39 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -39 + -1x + x2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + -1x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -1x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -1x + x2 = 0 + 39 -1x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -1x + x2 = 39 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. -1x + 0.25 + x2 = 39 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 39 + 0.25 Combine like terms: 39 + 0.25 = 39.25 0.25 + -1x + x2 = 39.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (x + 0.5) equal to 6.264982043 and -6.264982043.Subproblem 1
x + 0.5 = 6.264982043 Simplifying x + 0.5 = 6.264982043 Reorder the terms: 0.5 + x = 6.264982043 Solving 0.5 + x = 6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.264982043 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.264982043 + -0.5 x = 6.264982043 + -0.5 Combine like terms: 6.264982043 + -0.5 = 5.764982043 x = 5.764982043 Simplifying x = 5.764982043Subproblem 2
x + 0.5 = -6.264982043 Simplifying x + 0.5 = -6.264982043 Reorder the terms: 0.5 + x = -6.264982043 Solving 0.5 + x = -6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.264982043 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.264982043 + -0.5 x = -6.264982043 + -0.5 Combine like terms: -6.264982043 + -0.5 = -6.764982043 x = -6.764982043 Simplifying x = -6.764982043Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.764982043, -6.764982043}Solution
x = {0, 5.764982043, -6.764982043}
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