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Simplifying x2 + 13x = 9 Reorder the terms: 13x + x2 = 9 Solving 13x + x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 13x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 13x + x2 = 0 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 = 51.25 42.25 + 13x + x2 = 51.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + 6.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + 6.5 = 7.158910532 Simplifying x + 6.5 = 7.158910532 Reorder the terms: 6.5 + x = 7.158910532 Solving 6.5 + x = 7.158910532 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 = 7.158910532 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 7.158910532 + -6.5 x = 7.158910532 + -6.5 Combine like terms: 7.158910532 + -6.5 = 0.658910532 x = 0.658910532 Simplifying x = 0.658910532Subproblem 2
x + 6.5 = -7.158910532 Simplifying x + 6.5 = -7.158910532 Reorder the terms: 6.5 + x = -7.158910532 Solving 6.5 + x = -7.158910532 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 = -7.158910532 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -7.158910532 + -6.5 x = -7.158910532 + -6.5 Combine like terms: -7.158910532 + -6.5 = -13.658910532 x = -13.658910532 Simplifying x = -13.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.658910532, -13.658910532}
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