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Simplifying m2 + 10m = -7 Reorder the terms: 10m + m2 = -7 Solving 10m + m2 = -7 Solving for variable 'm'. Reorder the terms: 7 + 10m + m2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 10m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 10m + -7 + m2 = 0 + -7 Reorder the terms: 7 + -7 + 10m + m2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 10m + m2 = 0 + -7 10m + m2 = 0 + -7 Combine like terms: 0 + -7 = -7 10m + m2 = -7 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 = -7 + 25 Reorder the terms: 25 + 10m + m2 = -7 + 25 Combine like terms: -7 + 25 = 18 25 + 10m + m2 = 18 Factor a perfect square on the left side: (m + 5)(m + 5) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (m + 5) equal to 4.242640687 and -4.242640687.Subproblem 1
m + 5 = 4.242640687 Simplifying m + 5 = 4.242640687 Reorder the terms: 5 + m = 4.242640687 Solving 5 + m = 4.242640687 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 = 4.242640687 + -5 Combine like terms: 5 + -5 = 0 0 + m = 4.242640687 + -5 m = 4.242640687 + -5 Combine like terms: 4.242640687 + -5 = -0.757359313 m = -0.757359313 Simplifying m = -0.757359313Subproblem 2
m + 5 = -4.242640687 Simplifying m + 5 = -4.242640687 Reorder the terms: 5 + m = -4.242640687 Solving 5 + m = -4.242640687 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 = -4.242640687 + -5 Combine like terms: 5 + -5 = 0 0 + m = -4.242640687 + -5 m = -4.242640687 + -5 Combine like terms: -4.242640687 + -5 = -9.242640687 m = -9.242640687 Simplifying m = -9.242640687Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.757359313, -9.242640687}
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