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Simplifying x2 + -97x + 1127 = 0 Reorder the terms: 1127 + -97x + x2 = 0 Solving 1127 + -97x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1127' to each side of the equation. 1127 + -97x + -1127 + x2 = 0 + -1127 Reorder the terms: 1127 + -1127 + -97x + x2 = 0 + -1127 Combine like terms: 1127 + -1127 = 0 0 + -97x + x2 = 0 + -1127 -97x + x2 = 0 + -1127 Combine like terms: 0 + -1127 = -1127 -97x + x2 = -1127 The x term is -97x. Take half its coefficient (-48.5). Square it (2352.25) and add it to both sides. Add '2352.25' to each side of the equation. -97x + 2352.25 + x2 = -1127 + 2352.25 Reorder the terms: 2352.25 + -97x + x2 = -1127 + 2352.25 Combine like terms: -1127 + 2352.25 = 1225.25 2352.25 + -97x + x2 = 1225.25 Factor a perfect square on the left side: (x + -48.5)(x + -48.5) = 1225.25 Calculate the square root of the right side: 35.003571246 Break this problem into two subproblems by setting (x + -48.5) equal to 35.003571246 and -35.003571246.Subproblem 1
x + -48.5 = 35.003571246 Simplifying x + -48.5 = 35.003571246 Reorder the terms: -48.5 + x = 35.003571246 Solving -48.5 + x = 35.003571246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48.5' to each side of the equation. -48.5 + 48.5 + x = 35.003571246 + 48.5 Combine like terms: -48.5 + 48.5 = 0.0 0.0 + x = 35.003571246 + 48.5 x = 35.003571246 + 48.5 Combine like terms: 35.003571246 + 48.5 = 83.503571246 x = 83.503571246 Simplifying x = 83.503571246Subproblem 2
x + -48.5 = -35.003571246 Simplifying x + -48.5 = -35.003571246 Reorder the terms: -48.5 + x = -35.003571246 Solving -48.5 + x = -35.003571246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48.5' to each side of the equation. -48.5 + 48.5 + x = -35.003571246 + 48.5 Combine like terms: -48.5 + 48.5 = 0.0 0.0 + x = -35.003571246 + 48.5 x = -35.003571246 + 48.5 Combine like terms: -35.003571246 + 48.5 = 13.496428754 x = 13.496428754 Simplifying x = 13.496428754Solution
The solution to the problem is based on the solutions from the subproblems. x = {83.503571246, 13.496428754}
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