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Simplifying x2 + -55x + 552 = 0 Reorder the terms: 552 + -55x + x2 = 0 Solving 552 + -55x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-552' to each side of the equation. 552 + -55x + -552 + x2 = 0 + -552 Reorder the terms: 552 + -552 + -55x + x2 = 0 + -552 Combine like terms: 552 + -552 = 0 0 + -55x + x2 = 0 + -552 -55x + x2 = 0 + -552 Combine like terms: 0 + -552 = -552 -55x + x2 = -552 The x term is -55x. Take half its coefficient (-27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. -55x + 756.25 + x2 = -552 + 756.25 Reorder the terms: 756.25 + -55x + x2 = -552 + 756.25 Combine like terms: -552 + 756.25 = 204.25 756.25 + -55x + x2 = 204.25 Factor a perfect square on the left side: (x + -27.5)(x + -27.5) = 204.25 Calculate the square root of the right side: 14.291605928 Break this problem into two subproblems by setting (x + -27.5) equal to 14.291605928 and -14.291605928.Subproblem 1
x + -27.5 = 14.291605928 Simplifying x + -27.5 = 14.291605928 Reorder the terms: -27.5 + x = 14.291605928 Solving -27.5 + x = 14.291605928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = 14.291605928 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = 14.291605928 + 27.5 x = 14.291605928 + 27.5 Combine like terms: 14.291605928 + 27.5 = 41.791605928 x = 41.791605928 Simplifying x = 41.791605928Subproblem 2
x + -27.5 = -14.291605928 Simplifying x + -27.5 = -14.291605928 Reorder the terms: -27.5 + x = -14.291605928 Solving -27.5 + x = -14.291605928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = -14.291605928 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = -14.291605928 + 27.5 x = -14.291605928 + 27.5 Combine like terms: -14.291605928 + 27.5 = 13.208394072 x = 13.208394072 Simplifying x = 13.208394072Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.791605928, 13.208394072}
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