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Simplifying 10m2 = 2m + 3.14159 Reorder the terms: 10m2 = 3.14159 + 2m Solving 10m2 = 3.14159 + 2m Solving for variable 'm'. Reorder the terms: -3.14159 + -2m + 10m2 = 3.14159 + 2m + -3.14159 + -2m Reorder the terms: -3.14159 + -2m + 10m2 = 3.14159 + -3.14159 + 2m + -2m Combine like terms: 3.14159 + -3.14159 = 0.00000 -3.14159 + -2m + 10m2 = 0.00000 + 2m + -2m -3.14159 + -2m + 10m2 = 2m + -2m Combine like terms: 2m + -2m = 0 -3.14159 + -2m + 10m2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.314159 + -0.2m + m2 = 0 Move the constant term to the right: Add '0.314159' to each side of the equation. -0.314159 + -0.2m + 0.314159 + m2 = 0 + 0.314159 Reorder the terms: -0.314159 + 0.314159 + -0.2m + m2 = 0 + 0.314159 Combine like terms: -0.314159 + 0.314159 = 0.000000 0.000000 + -0.2m + m2 = 0 + 0.314159 -0.2m + m2 = 0 + 0.314159 Combine like terms: 0 + 0.314159 = 0.314159 -0.2m + m2 = 0.314159 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 = 0.314159 + 0.01 Reorder the terms: 0.01 + -0.2m + m2 = 0.314159 + 0.01 Combine like terms: 0.314159 + 0.01 = 0.324159 0.01 + -0.2m + m2 = 0.324159 Factor a perfect square on the left side: (m + -0.1)(m + -0.1) = 0.324159 Calculate the square root of the right side: 0.569349629 Break this problem into two subproblems by setting (m + -0.1) equal to 0.569349629 and -0.569349629.Subproblem 1
m + -0.1 = 0.569349629 Simplifying m + -0.1 = 0.569349629 Reorder the terms: -0.1 + m = 0.569349629 Solving -0.1 + m = 0.569349629 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 = 0.569349629 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + m = 0.569349629 + 0.1 m = 0.569349629 + 0.1 Combine like terms: 0.569349629 + 0.1 = 0.669349629 m = 0.669349629 Simplifying m = 0.669349629Subproblem 2
m + -0.1 = -0.569349629 Simplifying m + -0.1 = -0.569349629 Reorder the terms: -0.1 + m = -0.569349629 Solving -0.1 + m = -0.569349629 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 = -0.569349629 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + m = -0.569349629 + 0.1 m = -0.569349629 + 0.1 Combine like terms: -0.569349629 + 0.1 = -0.469349629 m = -0.469349629 Simplifying m = -0.469349629Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.669349629, -0.469349629}
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