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Simplifying m2 = -7m + -9 Reorder the terms: m2 = -9 + -7m Solving m2 = -9 + -7m Solving for variable 'm'. Reorder the terms: 9 + 7m + m2 = -9 + -7m + 9 + 7m Reorder the terms: 9 + 7m + m2 = -9 + 9 + -7m + 7m Combine like terms: -9 + 9 = 0 9 + 7m + m2 = 0 + -7m + 7m 9 + 7m + m2 = -7m + 7m Combine like terms: -7m + 7m = 0 9 + 7m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 7m + -9 + m2 = 0 + -9 Reorder the terms: 9 + -9 + 7m + m2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 7m + m2 = 0 + -9 7m + m2 = 0 + -9 Combine like terms: 0 + -9 = -9 7m + m2 = -9 The m term is 7m. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7m + 12.25 + m2 = -9 + 12.25 Reorder the terms: 12.25 + 7m + m2 = -9 + 12.25 Combine like terms: -9 + 12.25 = 3.25 12.25 + 7m + m2 = 3.25 Factor a perfect square on the left side: (m + 3.5)(m + 3.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (m + 3.5) equal to 1.802775638 and -1.802775638.Subproblem 1
m + 3.5 = 1.802775638 Simplifying m + 3.5 = 1.802775638 Reorder the terms: 3.5 + m = 1.802775638 Solving 3.5 + m = 1.802775638 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = 1.802775638 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = 1.802775638 + -3.5 m = 1.802775638 + -3.5 Combine like terms: 1.802775638 + -3.5 = -1.697224362 m = -1.697224362 Simplifying m = -1.697224362Subproblem 2
m + 3.5 = -1.802775638 Simplifying m + 3.5 = -1.802775638 Reorder the terms: 3.5 + m = -1.802775638 Solving 3.5 + m = -1.802775638 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = -1.802775638 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = -1.802775638 + -3.5 m = -1.802775638 + -3.5 Combine like terms: -1.802775638 + -3.5 = -5.302775638 m = -5.302775638 Simplifying m = -5.302775638Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.697224362, -5.302775638}
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