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Simplifying 11x + x2 = 153 Solving 11x + x2 = 153 Solving for variable 'x'. Reorder the terms: -153 + 11x + x2 = 153 + -153 Combine like terms: 153 + -153 = 0 -153 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '153' to each side of the equation. -153 + 11x + 153 + x2 = 0 + 153 Reorder the terms: -153 + 153 + 11x + x2 = 0 + 153 Combine like terms: -153 + 153 = 0 0 + 11x + x2 = 0 + 153 11x + x2 = 0 + 153 Combine like terms: 0 + 153 = 153 11x + x2 = 153 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 153 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 153 + 30.25 Combine like terms: 153 + 30.25 = 183.25 30.25 + 11x + x2 = 183.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 183.25 Calculate the square root of the right side: 13.536986371 Break this problem into two subproblems by setting (x + 5.5) equal to 13.536986371 and -13.536986371.Subproblem 1
x + 5.5 = 13.536986371 Simplifying x + 5.5 = 13.536986371 Reorder the terms: 5.5 + x = 13.536986371 Solving 5.5 + x = 13.536986371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 13.536986371 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 13.536986371 + -5.5 x = 13.536986371 + -5.5 Combine like terms: 13.536986371 + -5.5 = 8.036986371 x = 8.036986371 Simplifying x = 8.036986371Subproblem 2
x + 5.5 = -13.536986371 Simplifying x + 5.5 = -13.536986371 Reorder the terms: 5.5 + x = -13.536986371 Solving 5.5 + x = -13.536986371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -13.536986371 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -13.536986371 + -5.5 x = -13.536986371 + -5.5 Combine like terms: -13.536986371 + -5.5 = -19.036986371 x = -19.036986371 Simplifying x = -19.036986371Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.036986371, -19.036986371}
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