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Simplifying 2x3 + 26x2 + 8x = 0 Reorder the terms: 8x + 26x2 + 2x3 = 0 Solving 8x + 26x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(4 + 13x + x2) = 0 Ignore the factor 2.Subproblem 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 '(4 + 13x + x2)' equal to zero and attempt to solve: Simplifying 4 + 13x + x2 = 0 Solving 4 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 13x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 13x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 13x + x2 = 0 + -4 13x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 13x + x2 = -4 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = -4 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -4 + 42.25 Combine like terms: -4 + 42.25 = 38.25 42.25 + 13x + x2 = 38.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x + 6.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x + 6.5 = 6.184658438 Simplifying x + 6.5 = 6.184658438 Reorder the terms: 6.5 + x = 6.184658438 Solving 6.5 + x = 6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 6.184658438 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 6.184658438 + -6.5 x = 6.184658438 + -6.5 Combine like terms: 6.184658438 + -6.5 = -0.315341562 x = -0.315341562 Simplifying x = -0.315341562Subproblem 2
x + 6.5 = -6.184658438 Simplifying x + 6.5 = -6.184658438 Reorder the terms: 6.5 + x = -6.184658438 Solving 6.5 + x = -6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -6.184658438 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -6.184658438 + -6.5 x = -6.184658438 + -6.5 Combine like terms: -6.184658438 + -6.5 = -12.684658438 x = -12.684658438 Simplifying x = -12.684658438Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.315341562, -12.684658438}Solution
x = {0, -0.315341562, -12.684658438}
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