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Simplifying 2x2 + -264x + 989 = 0 Reorder the terms: 989 + -264x + 2x2 = 0 Solving 989 + -264x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 494.5 + -132x + x2 = 0 Move the constant term to the right: Add '-494.5' to each side of the equation. 494.5 + -132x + -494.5 + x2 = 0 + -494.5 Reorder the terms: 494.5 + -494.5 + -132x + x2 = 0 + -494.5 Combine like terms: 494.5 + -494.5 = 0.0 0.0 + -132x + x2 = 0 + -494.5 -132x + x2 = 0 + -494.5 Combine like terms: 0 + -494.5 = -494.5 -132x + x2 = -494.5 The x term is -132x. Take half its coefficient (-66). Square it (4356) and add it to both sides. Add '4356' to each side of the equation. -132x + 4356 + x2 = -494.5 + 4356 Reorder the terms: 4356 + -132x + x2 = -494.5 + 4356 Combine like terms: -494.5 + 4356 = 3861.5 4356 + -132x + x2 = 3861.5 Factor a perfect square on the left side: (x + -66)(x + -66) = 3861.5 Calculate the square root of the right side: 62.140968773 Break this problem into two subproblems by setting (x + -66) equal to 62.140968773 and -62.140968773.Subproblem 1
x + -66 = 62.140968773 Simplifying x + -66 = 62.140968773 Reorder the terms: -66 + x = 62.140968773 Solving -66 + x = 62.140968773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66' to each side of the equation. -66 + 66 + x = 62.140968773 + 66 Combine like terms: -66 + 66 = 0 0 + x = 62.140968773 + 66 x = 62.140968773 + 66 Combine like terms: 62.140968773 + 66 = 128.140968773 x = 128.140968773 Simplifying x = 128.140968773Subproblem 2
x + -66 = -62.140968773 Simplifying x + -66 = -62.140968773 Reorder the terms: -66 + x = -62.140968773 Solving -66 + x = -62.140968773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66' to each side of the equation. -66 + 66 + x = -62.140968773 + 66 Combine like terms: -66 + 66 = 0 0 + x = -62.140968773 + 66 x = -62.140968773 + 66 Combine like terms: -62.140968773 + 66 = 3.859031227 x = 3.859031227 Simplifying x = 3.859031227Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.140968773, 3.859031227}
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