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Simplifying 129x + -1x2 = 77 Solving 129x + -1x2 = 77 Solving for variable 'x'. Reorder the terms: -77 + 129x + -1x2 = 77 + -77 Combine like terms: 77 + -77 = 0 -77 + 129x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 77 + -129x + x2 = 0 Move the constant term to the right: Add '-77' to each side of the equation. 77 + -129x + -77 + x2 = 0 + -77 Reorder the terms: 77 + -77 + -129x + x2 = 0 + -77 Combine like terms: 77 + -77 = 0 0 + -129x + x2 = 0 + -77 -129x + x2 = 0 + -77 Combine like terms: 0 + -77 = -77 -129x + x2 = -77 The x term is -129x. Take half its coefficient (-64.5). Square it (4160.25) and add it to both sides. Add '4160.25' to each side of the equation. -129x + 4160.25 + x2 = -77 + 4160.25 Reorder the terms: 4160.25 + -129x + x2 = -77 + 4160.25 Combine like terms: -77 + 4160.25 = 4083.25 4160.25 + -129x + x2 = 4083.25 Factor a perfect square on the left side: (x + -64.5)(x + -64.5) = 4083.25 Calculate the square root of the right side: 63.900312988 Break this problem into two subproblems by setting (x + -64.5) equal to 63.900312988 and -63.900312988.Subproblem 1
x + -64.5 = 63.900312988 Simplifying x + -64.5 = 63.900312988 Reorder the terms: -64.5 + x = 63.900312988 Solving -64.5 + x = 63.900312988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '64.5' to each side of the equation. -64.5 + 64.5 + x = 63.900312988 + 64.5 Combine like terms: -64.5 + 64.5 = 0.0 0.0 + x = 63.900312988 + 64.5 x = 63.900312988 + 64.5 Combine like terms: 63.900312988 + 64.5 = 128.400312988 x = 128.400312988 Simplifying x = 128.400312988Subproblem 2
x + -64.5 = -63.900312988 Simplifying x + -64.5 = -63.900312988 Reorder the terms: -64.5 + x = -63.900312988 Solving -64.5 + x = -63.900312988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '64.5' to each side of the equation. -64.5 + 64.5 + x = -63.900312988 + 64.5 Combine like terms: -64.5 + 64.5 = 0.0 0.0 + x = -63.900312988 + 64.5 x = -63.900312988 + 64.5 Combine like terms: -63.900312988 + 64.5 = 0.599687012 x = 0.599687012 Simplifying x = 0.599687012Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.400312988, 0.599687012}
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