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Simplifying x2 + 13x + 9 = 0 Reorder the terms: 9 + 13x + x2 = 0 Solving 9 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 13x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 13x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 13x + x2 = 0 + -9 13x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 13x + x2 = -9 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 = -9 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -9 + 42.25 Combine like terms: -9 + 42.25 = 33.25 42.25 + 13x + x2 = 33.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x + 6.5) equal to 5.766281297 and -5.766281297.Subproblem 1
x + 6.5 = 5.766281297 Simplifying x + 6.5 = 5.766281297 Reorder the terms: 6.5 + x = 5.766281297 Solving 6.5 + x = 5.766281297 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 = 5.766281297 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 5.766281297 + -6.5 x = 5.766281297 + -6.5 Combine like terms: 5.766281297 + -6.5 = -0.733718703 x = -0.733718703 Simplifying x = -0.733718703Subproblem 2
x + 6.5 = -5.766281297 Simplifying x + 6.5 = -5.766281297 Reorder the terms: 6.5 + x = -5.766281297 Solving 6.5 + x = -5.766281297 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 = -5.766281297 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -5.766281297 + -6.5 x = -5.766281297 + -6.5 Combine like terms: -5.766281297 + -6.5 = -12.266281297 x = -12.266281297 Simplifying x = -12.266281297Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.733718703, -12.266281297}
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