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Simplifying -1m2 + 11m + -27 = 0 Reorder the terms: -27 + 11m + -1m2 = 0 Solving -27 + 11m + -1m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 27 + -11m + m2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -11m + -27 + m2 = 0 + -27 Reorder the terms: 27 + -27 + -11m + m2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -11m + m2 = 0 + -27 -11m + m2 = 0 + -27 Combine like terms: 0 + -27 = -27 -11m + m2 = -27 The m term is -11m. 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. -11m + 30.25 + m2 = -27 + 30.25 Reorder the terms: 30.25 + -11m + m2 = -27 + 30.25 Combine like terms: -27 + 30.25 = 3.25 30.25 + -11m + m2 = 3.25 Factor a perfect square on the left side: (m + -5.5)(m + -5.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (m + -5.5) equal to 1.802775638 and -1.802775638.Subproblem 1
m + -5.5 = 1.802775638 Simplifying m + -5.5 = 1.802775638 Reorder the terms: -5.5 + m = 1.802775638 Solving -5.5 + m = 1.802775638 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + m = 1.802775638 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + m = 1.802775638 + 5.5 m = 1.802775638 + 5.5 Combine like terms: 1.802775638 + 5.5 = 7.302775638 m = 7.302775638 Simplifying m = 7.302775638Subproblem 2
m + -5.5 = -1.802775638 Simplifying m + -5.5 = -1.802775638 Reorder the terms: -5.5 + m = -1.802775638 Solving -5.5 + m = -1.802775638 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + m = -1.802775638 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + m = -1.802775638 + 5.5 m = -1.802775638 + 5.5 Combine like terms: -1.802775638 + 5.5 = 3.697224362 m = 3.697224362 Simplifying m = 3.697224362Solution
The solution to the problem is based on the solutions from the subproblems. m = {7.302775638, 3.697224362}
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