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Simplifying 10m2 + 2m = 3 Reorder the terms: 2m + 10m2 = 3 Solving 2m + 10m2 = 3 Solving for variable 'm'. Reorder the terms: -3 + 2m + 10m2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 2m + 10m2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + 0.2m + m2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.2m + 0.3 + m2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.2m + m2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.2m + m2 = 0 + 0.3 0.2m + m2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 0.2m + m2 = 0.3 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 = 0.3 + 0.01 Reorder the terms: 0.01 + 0.2m + m2 = 0.3 + 0.01 Combine like terms: 0.3 + 0.01 = 0.31 0.01 + 0.2m + m2 = 0.31 Factor a perfect square on the left side: (m + 0.1)(m + 0.1) = 0.31 Calculate the square root of the right side: 0.556776436 Break this problem into two subproblems by setting (m + 0.1) equal to 0.556776436 and -0.556776436.Subproblem 1
m + 0.1 = 0.556776436 Simplifying m + 0.1 = 0.556776436 Reorder the terms: 0.1 + m = 0.556776436 Solving 0.1 + m = 0.556776436 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 = 0.556776436 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + m = 0.556776436 + -0.1 m = 0.556776436 + -0.1 Combine like terms: 0.556776436 + -0.1 = 0.456776436 m = 0.456776436 Simplifying m = 0.456776436Subproblem 2
m + 0.1 = -0.556776436 Simplifying m + 0.1 = -0.556776436 Reorder the terms: 0.1 + m = -0.556776436 Solving 0.1 + m = -0.556776436 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 = -0.556776436 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + m = -0.556776436 + -0.1 m = -0.556776436 + -0.1 Combine like terms: -0.556776436 + -0.1 = -0.656776436 m = -0.656776436 Simplifying m = -0.656776436Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.456776436, -0.656776436}
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