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Simplifying 10m2 + 2m = 11 Reorder the terms: 2m + 10m2 = 11 Solving 2m + 10m2 = 11 Solving for variable 'm'. Reorder the terms: -11 + 2m + 10m2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 2m + 10m2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.1 + 0.2m + m2 = 0 Move the constant term to the right: Add '1.1' to each side of the equation. -1.1 + 0.2m + 1.1 + m2 = 0 + 1.1 Reorder the terms: -1.1 + 1.1 + 0.2m + m2 = 0 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + 0.2m + m2 = 0 + 1.1 0.2m + m2 = 0 + 1.1 Combine like terms: 0 + 1.1 = 1.1 0.2m + m2 = 1.1 The m term is 0.2m. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2m + 0.01 + m2 = 1.1 + 0.01 Reorder the terms: 0.01 + 0.2m + m2 = 1.1 + 0.01 Combine like terms: 1.1 + 0.01 = 1.11 0.01 + 0.2m + m2 = 1.11 Factor a perfect square on the left side: (m + 0.1)(m + 0.1) = 1.11 Calculate the square root of the right side: 1.053565375 Break this problem into two subproblems by setting (m + 0.1) equal to 1.053565375 and -1.053565375.Subproblem 1
m + 0.1 = 1.053565375 Simplifying m + 0.1 = 1.053565375 Reorder the terms: 0.1 + m = 1.053565375 Solving 0.1 + m = 1.053565375 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + m = 1.053565375 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + m = 1.053565375 + -0.1 m = 1.053565375 + -0.1 Combine like terms: 1.053565375 + -0.1 = 0.953565375 m = 0.953565375 Simplifying m = 0.953565375Subproblem 2
m + 0.1 = -1.053565375 Simplifying m + 0.1 = -1.053565375 Reorder the terms: 0.1 + m = -1.053565375 Solving 0.1 + m = -1.053565375 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + m = -1.053565375 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + m = -1.053565375 + -0.1 m = -1.053565375 + -0.1 Combine like terms: -1.053565375 + -0.1 = -1.153565375 m = -1.153565375 Simplifying m = -1.153565375Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.953565375, -1.153565375}
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