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Simplifying x2 + 13x + 40 = 166.75 Reorder the terms: 40 + 13x + x2 = 166.75 Solving 40 + 13x + x2 = 166.75 Solving for variable 'x'. Reorder the terms: 40 + -166.75 + 13x + x2 = 166.75 + -166.75 Combine like terms: 40 + -166.75 = -126.75 -126.75 + 13x + x2 = 166.75 + -166.75 Combine like terms: 166.75 + -166.75 = 0.00 -126.75 + 13x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '126.75' to each side of the equation. -126.75 + 13x + 126.75 + x2 = 0.00 + 126.75 Reorder the terms: -126.75 + 126.75 + 13x + x2 = 0.00 + 126.75 Combine like terms: -126.75 + 126.75 = 0.00 0.00 + 13x + x2 = 0.00 + 126.75 13x + x2 = 0.00 + 126.75 Combine like terms: 0.00 + 126.75 = 126.75 13x + x2 = 126.75 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 = 126.75 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 126.75 + 42.25 Combine like terms: 126.75 + 42.25 = 169 42.25 + 13x + x2 = 169 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 169 Calculate the square root of the right side: 13 Break this problem into two subproblems by setting (x + 6.5) equal to 13 and -13.Subproblem 1
x + 6.5 = 13 Simplifying x + 6.5 = 13 Reorder the terms: 6.5 + x = 13 Solving 6.5 + x = 13 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 = 13 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 13 + -6.5 x = 13 + -6.5 Combine like terms: 13 + -6.5 = 6.5 x = 6.5 Simplifying x = 6.5Subproblem 2
x + 6.5 = -13 Simplifying x + 6.5 = -13 Reorder the terms: 6.5 + x = -13 Solving 6.5 + x = -13 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 = -13 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -13 + -6.5 x = -13 + -6.5 Combine like terms: -13 + -6.5 = -19.5 x = -19.5 Simplifying x = -19.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.5, -19.5}
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