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Simplifying 0 = x2 + 13x + 14 Reorder the terms: 0 = 14 + 13x + x2 Solving 0 = 14 + 13x + x2 Solving for variable 'x'. Combine like terms: 0 + -14 = -14 -14 + -13x + -1x2 = 14 + 13x + x2 + -14 + -13x + -1x2 Reorder the terms: -14 + -13x + -1x2 = 14 + -14 + 13x + -13x + x2 + -1x2 Combine like terms: 14 + -14 = 0 -14 + -13x + -1x2 = 0 + 13x + -13x + x2 + -1x2 -14 + -13x + -1x2 = 13x + -13x + x2 + -1x2 Combine like terms: 13x + -13x = 0 -14 + -13x + -1x2 = 0 + x2 + -1x2 -14 + -13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -14 + -13x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(14 + 13x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(14 + 13x + x2)' equal to zero and attempt to solve: Simplifying 14 + 13x + x2 = 0 Solving 14 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 13x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 13x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 13x + x2 = 0 + -14 13x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 13x + x2 = -14 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 = -14 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -14 + 42.25 Combine like terms: -14 + 42.25 = 28.25 42.25 + 13x + x2 = 28.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + 6.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + 6.5 = 5.315072906 Simplifying x + 6.5 = 5.315072906 Reorder the terms: 6.5 + x = 5.315072906 Solving 6.5 + x = 5.315072906 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 = 5.315072906 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 5.315072906 + -6.5 x = 5.315072906 + -6.5 Combine like terms: 5.315072906 + -6.5 = -1.184927094 x = -1.184927094 Simplifying x = -1.184927094Subproblem 2
x + 6.5 = -5.315072906 Simplifying x + 6.5 = -5.315072906 Reorder the terms: 6.5 + x = -5.315072906 Solving 6.5 + x = -5.315072906 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 = -5.315072906 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -5.315072906 + -6.5 x = -5.315072906 + -6.5 Combine like terms: -5.315072906 + -6.5 = -11.815072906 x = -11.815072906 Simplifying x = -11.815072906Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.184927094, -11.815072906}Solution
x = {-1.184927094, -11.815072906}
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