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Simplifying 4x3 + 26x2 + 2x = 0 Reorder the terms: 2x + 26x2 + 4x3 = 0 Solving 2x + 26x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(1 + 13x + 2x2) = 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 '(1 + 13x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + 13x + 2x2 = 0 Solving 1 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + 6.5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 6.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 6.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 6.5x + x2 = 0 + -0.5 6.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 6.5x + x2 = -0.5 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = -0.5 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -0.5 + 10.5625 Combine like terms: -0.5 + 10.5625 = 10.0625 10.5625 + 6.5x + x2 = 10.0625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (x + 3.25) equal to 3.172144385 and -3.172144385.Subproblem 1
x + 3.25 = 3.172144385 Simplifying x + 3.25 = 3.172144385 Reorder the terms: 3.25 + x = 3.172144385 Solving 3.25 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 3.172144385 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.172144385 + -3.25 x = 3.172144385 + -3.25 Combine like terms: 3.172144385 + -3.25 = -0.077855615 x = -0.077855615 Simplifying x = -0.077855615Subproblem 2
x + 3.25 = -3.172144385 Simplifying x + 3.25 = -3.172144385 Reorder the terms: 3.25 + x = -3.172144385 Solving 3.25 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -3.172144385 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.172144385 + -3.25 x = -3.172144385 + -3.25 Combine like terms: -3.172144385 + -3.25 = -6.422144385 x = -6.422144385 Simplifying x = -6.422144385Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.077855615, -6.422144385}Solution
x = {0, -0.077855615, -6.422144385}
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