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Simplifying 2x3 + 13x2 + 3x = 0 Reorder the terms: 3x + 13x2 + 2x3 = 0 Solving 3x + 13x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + 13x + 2x2) = 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 '(3 + 13x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + 13x + 2x2 = 0 Solving 3 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 6.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 6.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 6.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 6.5x + x2 = 0 + -1.5 6.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 6.5x + x2 = -1.5 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 = -1.5 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -1.5 + 10.5625 Combine like terms: -1.5 + 10.5625 = 9.0625 10.5625 + 6.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + 3.25) equal to 3.010398645 and -3.010398645.Subproblem 1
x + 3.25 = 3.010398645 Simplifying x + 3.25 = 3.010398645 Reorder the terms: 3.25 + x = 3.010398645 Solving 3.25 + x = 3.010398645 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 = 3.010398645 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.010398645 + -3.25 x = 3.010398645 + -3.25 Combine like terms: 3.010398645 + -3.25 = -0.239601355 x = -0.239601355 Simplifying x = -0.239601355Subproblem 2
x + 3.25 = -3.010398645 Simplifying x + 3.25 = -3.010398645 Reorder the terms: 3.25 + x = -3.010398645 Solving 3.25 + x = -3.010398645 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 = -3.010398645 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.010398645 + -3.25 x = -3.010398645 + -3.25 Combine like terms: -3.010398645 + -3.25 = -6.260398645 x = -6.260398645 Simplifying x = -6.260398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.239601355, -6.260398645}Solution
x = {0, -0.239601355, -6.260398645}
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