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Simplifying x2 + 33x = 142 Reorder the terms: 33x + x2 = 142 Solving 33x + x2 = 142 Solving for variable 'x'. Reorder the terms: -142 + 33x + x2 = 142 + -142 Combine like terms: 142 + -142 = 0 -142 + 33x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '142' to each side of the equation. -142 + 33x + 142 + x2 = 0 + 142 Reorder the terms: -142 + 142 + 33x + x2 = 0 + 142 Combine like terms: -142 + 142 = 0 0 + 33x + x2 = 0 + 142 33x + x2 = 0 + 142 Combine like terms: 0 + 142 = 142 33x + x2 = 142 The x term is 33x. Take half its coefficient (16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. 33x + 272.25 + x2 = 142 + 272.25 Reorder the terms: 272.25 + 33x + x2 = 142 + 272.25 Combine like terms: 142 + 272.25 = 414.25 272.25 + 33x + x2 = 414.25 Factor a perfect square on the left side: (x + 16.5)(x + 16.5) = 414.25 Calculate the square root of the right side: 20.353132437 Break this problem into two subproblems by setting (x + 16.5) equal to 20.353132437 and -20.353132437.Subproblem 1
x + 16.5 = 20.353132437 Simplifying x + 16.5 = 20.353132437 Reorder the terms: 16.5 + x = 20.353132437 Solving 16.5 + x = 20.353132437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = 20.353132437 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 20.353132437 + -16.5 x = 20.353132437 + -16.5 Combine like terms: 20.353132437 + -16.5 = 3.853132437 x = 3.853132437 Simplifying x = 3.853132437Subproblem 2
x + 16.5 = -20.353132437 Simplifying x + 16.5 = -20.353132437 Reorder the terms: 16.5 + x = -20.353132437 Solving 16.5 + x = -20.353132437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = -20.353132437 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -20.353132437 + -16.5 x = -20.353132437 + -16.5 Combine like terms: -20.353132437 + -16.5 = -36.853132437 x = -36.853132437 Simplifying x = -36.853132437Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.853132437, -36.853132437}
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