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Simplifying x2 + 13x = 154 Reorder the terms: 13x + x2 = 154 Solving 13x + x2 = 154 Solving for variable 'x'. Reorder the terms: -154 + 13x + x2 = 154 + -154 Combine like terms: 154 + -154 = 0 -154 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '154' to each side of the equation. -154 + 13x + 154 + x2 = 0 + 154 Reorder the terms: -154 + 154 + 13x + x2 = 0 + 154 Combine like terms: -154 + 154 = 0 0 + 13x + x2 = 0 + 154 13x + x2 = 0 + 154 Combine like terms: 0 + 154 = 154 13x + x2 = 154 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 = 154 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 154 + 42.25 Combine like terms: 154 + 42.25 = 196.25 42.25 + 13x + x2 = 196.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 196.25 Calculate the square root of the right side: 14.008925726 Break this problem into two subproblems by setting (x + 6.5) equal to 14.008925726 and -14.008925726.Subproblem 1
x + 6.5 = 14.008925726 Simplifying x + 6.5 = 14.008925726 Reorder the terms: 6.5 + x = 14.008925726 Solving 6.5 + x = 14.008925726 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 = 14.008925726 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 14.008925726 + -6.5 x = 14.008925726 + -6.5 Combine like terms: 14.008925726 + -6.5 = 7.508925726 x = 7.508925726 Simplifying x = 7.508925726Subproblem 2
x + 6.5 = -14.008925726 Simplifying x + 6.5 = -14.008925726 Reorder the terms: 6.5 + x = -14.008925726 Solving 6.5 + x = -14.008925726 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 = -14.008925726 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -14.008925726 + -6.5 x = -14.008925726 + -6.5 Combine like terms: -14.008925726 + -6.5 = -20.508925726 x = -20.508925726 Simplifying x = -20.508925726Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.508925726, -20.508925726}
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