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Simplifying -1x2 + 11x = 27 Reorder the terms: 11x + -1x2 = 27 Solving 11x + -1x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + 11x + -1x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 27 + -11x + x2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -11x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -11x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -11x + x2 = 0 + -27 -11x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -11x + x2 = -27 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -27 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -27 + 30.25 Combine like terms: -27 + 30.25 = 3.25 30.25 + -11x + x2 = 3.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + -5.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + -5.5 = 1.802775638 Simplifying x + -5.5 = 1.802775638 Reorder the terms: -5.5 + x = 1.802775638 Solving -5.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 1.802775638 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 1.802775638 + 5.5 x = 1.802775638 + 5.5 Combine like terms: 1.802775638 + 5.5 = 7.302775638 x = 7.302775638 Simplifying x = 7.302775638Subproblem 2
x + -5.5 = -1.802775638 Simplifying x + -5.5 = -1.802775638 Reorder the terms: -5.5 + x = -1.802775638 Solving -5.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -1.802775638 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -1.802775638 + 5.5 x = -1.802775638 + 5.5 Combine like terms: -1.802775638 + 5.5 = 3.697224362 x = 3.697224362 Simplifying x = 3.697224362Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.302775638, 3.697224362}
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