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Simplifying m2 + 17m + 22 = 0 Reorder the terms: 22 + 17m + m2 = 0 Solving 22 + 17m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 17m + -22 + m2 = 0 + -22 Reorder the terms: 22 + -22 + 17m + m2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 17m + m2 = 0 + -22 17m + m2 = 0 + -22 Combine like terms: 0 + -22 = -22 17m + m2 = -22 The m term is 17m. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17m + 72.25 + m2 = -22 + 72.25 Reorder the terms: 72.25 + 17m + m2 = -22 + 72.25 Combine like terms: -22 + 72.25 = 50.25 72.25 + 17m + m2 = 50.25 Factor a perfect square on the left side: (m + 8.5)(m + 8.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (m + 8.5) equal to 7.088723439 and -7.088723439.Subproblem 1
m + 8.5 = 7.088723439 Simplifying m + 8.5 = 7.088723439 Reorder the terms: 8.5 + m = 7.088723439 Solving 8.5 + m = 7.088723439 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + m = 7.088723439 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + m = 7.088723439 + -8.5 m = 7.088723439 + -8.5 Combine like terms: 7.088723439 + -8.5 = -1.411276561 m = -1.411276561 Simplifying m = -1.411276561Subproblem 2
m + 8.5 = -7.088723439 Simplifying m + 8.5 = -7.088723439 Reorder the terms: 8.5 + m = -7.088723439 Solving 8.5 + m = -7.088723439 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + m = -7.088723439 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + m = -7.088723439 + -8.5 m = -7.088723439 + -8.5 Combine like terms: -7.088723439 + -8.5 = -15.588723439 m = -15.588723439 Simplifying m = -15.588723439Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.411276561, -15.588723439}
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