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Simplifying x2 + 13x + 3 = 0 Reorder the terms: 3 + 13x + x2 = 0 Solving 3 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 13x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 13x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 13x + x2 = 0 + -3 13x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 13x + x2 = -3 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 = -3 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -3 + 42.25 Combine like terms: -3 + 42.25 = 39.25 42.25 + 13x + x2 = 39.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (x + 6.5) equal to 6.264982043 and -6.264982043.Subproblem 1
x + 6.5 = 6.264982043 Simplifying x + 6.5 = 6.264982043 Reorder the terms: 6.5 + x = 6.264982043 Solving 6.5 + x = 6.264982043 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 = 6.264982043 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 6.264982043 + -6.5 x = 6.264982043 + -6.5 Combine like terms: 6.264982043 + -6.5 = -0.235017957 x = -0.235017957 Simplifying x = -0.235017957Subproblem 2
x + 6.5 = -6.264982043 Simplifying x + 6.5 = -6.264982043 Reorder the terms: 6.5 + x = -6.264982043 Solving 6.5 + x = -6.264982043 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 = -6.264982043 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -6.264982043 + -6.5 x = -6.264982043 + -6.5 Combine like terms: -6.264982043 + -6.5 = -12.764982043 x = -12.764982043 Simplifying x = -12.764982043Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.235017957, -12.764982043}
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