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Simplifying x2 + 13x + 39 = 0 Reorder the terms: 39 + 13x + x2 = 0 Solving 39 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + 13x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + 13x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 13x + x2 = 0 + -39 13x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 13x + x2 = -39 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 = -39 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -39 + 42.25 Combine like terms: -39 + 42.25 = 3.25 42.25 + 13x + x2 = 3.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 6.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 6.5 = 1.802775638 Simplifying x + 6.5 = 1.802775638 Reorder the terms: 6.5 + x = 1.802775638 Solving 6.5 + x = 1.802775638 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 = 1.802775638 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 1.802775638 + -6.5 x = 1.802775638 + -6.5 Combine like terms: 1.802775638 + -6.5 = -4.697224362 x = -4.697224362 Simplifying x = -4.697224362Subproblem 2
x + 6.5 = -1.802775638 Simplifying x + 6.5 = -1.802775638 Reorder the terms: 6.5 + x = -1.802775638 Solving 6.5 + x = -1.802775638 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 = -1.802775638 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -1.802775638 + -6.5 x = -1.802775638 + -6.5 Combine like terms: -1.802775638 + -6.5 = -8.302775638 x = -8.302775638 Simplifying x = -8.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.697224362, -8.302775638}
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