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Simplifying m2 + 10m = 9 Reorder the terms: 10m + m2 = 9 Solving 10m + m2 = 9 Solving for variable 'm'. Reorder the terms: -9 + 10m + m2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 10m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 10m + 9 + m2 = 0 + 9 Reorder the terms: -9 + 9 + 10m + m2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 10m + m2 = 0 + 9 10m + m2 = 0 + 9 Combine like terms: 0 + 9 = 9 10m + m2 = 9 The m term is 10m. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10m + 25 + m2 = 9 + 25 Reorder the terms: 25 + 10m + m2 = 9 + 25 Combine like terms: 9 + 25 = 34 25 + 10m + m2 = 34 Factor a perfect square on the left side: (m + 5)(m + 5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (m + 5) equal to 5.830951895 and -5.830951895.Subproblem 1
m + 5 = 5.830951895 Simplifying m + 5 = 5.830951895 Reorder the terms: 5 + m = 5.830951895 Solving 5 + m = 5.830951895 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m = 5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + m = 5.830951895 + -5 m = 5.830951895 + -5 Combine like terms: 5.830951895 + -5 = 0.830951895 m = 0.830951895 Simplifying m = 0.830951895Subproblem 2
m + 5 = -5.830951895 Simplifying m + 5 = -5.830951895 Reorder the terms: 5 + m = -5.830951895 Solving 5 + m = -5.830951895 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m = -5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + m = -5.830951895 + -5 m = -5.830951895 + -5 Combine like terms: -5.830951895 + -5 = -10.830951895 m = -10.830951895 Simplifying m = -10.830951895Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.830951895, -10.830951895}
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