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Simplifying x2 + 13x + -16 = 0 Reorder the terms: -16 + 13x + x2 = 0 Solving -16 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 13x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 13x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 13x + x2 = 0 + 16 13x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 13x + x2 = 16 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 = 16 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 16 + 42.25 Combine like terms: 16 + 42.25 = 58.25 42.25 + 13x + x2 = 58.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (x + 6.5) equal to 7.632168761 and -7.632168761.Subproblem 1
x + 6.5 = 7.632168761 Simplifying x + 6.5 = 7.632168761 Reorder the terms: 6.5 + x = 7.632168761 Solving 6.5 + x = 7.632168761 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 = 7.632168761 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 7.632168761 + -6.5 x = 7.632168761 + -6.5 Combine like terms: 7.632168761 + -6.5 = 1.132168761 x = 1.132168761 Simplifying x = 1.132168761Subproblem 2
x + 6.5 = -7.632168761 Simplifying x + 6.5 = -7.632168761 Reorder the terms: 6.5 + x = -7.632168761 Solving 6.5 + x = -7.632168761 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 = -7.632168761 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -7.632168761 + -6.5 x = -7.632168761 + -6.5 Combine like terms: -7.632168761 + -6.5 = -14.132168761 x = -14.132168761 Simplifying x = -14.132168761Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.132168761, -14.132168761}
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