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Simplifying 10m2 + 3m + -21 = 0 Reorder the terms: -21 + 3m + 10m2 = 0 Solving -21 + 3m + 10m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.1 + 0.3m + m2 = 0 Move the constant term to the right: Add '2.1' to each side of the equation. -2.1 + 0.3m + 2.1 + m2 = 0 + 2.1 Reorder the terms: -2.1 + 2.1 + 0.3m + m2 = 0 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + 0.3m + m2 = 0 + 2.1 0.3m + m2 = 0 + 2.1 Combine like terms: 0 + 2.1 = 2.1 0.3m + m2 = 2.1 The m term is 0.3m. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3m + 0.0225 + m2 = 2.1 + 0.0225 Reorder the terms: 0.0225 + 0.3m + m2 = 2.1 + 0.0225 Combine like terms: 2.1 + 0.0225 = 2.1225 0.0225 + 0.3m + m2 = 2.1225 Factor a perfect square on the left side: (m + 0.15)(m + 0.15) = 2.1225 Calculate the square root of the right side: 1.456880228 Break this problem into two subproblems by setting (m + 0.15) equal to 1.456880228 and -1.456880228.Subproblem 1
m + 0.15 = 1.456880228 Simplifying m + 0.15 = 1.456880228 Reorder the terms: 0.15 + m = 1.456880228 Solving 0.15 + m = 1.456880228 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + m = 1.456880228 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + m = 1.456880228 + -0.15 m = 1.456880228 + -0.15 Combine like terms: 1.456880228 + -0.15 = 1.306880228 m = 1.306880228 Simplifying m = 1.306880228Subproblem 2
m + 0.15 = -1.456880228 Simplifying m + 0.15 = -1.456880228 Reorder the terms: 0.15 + m = -1.456880228 Solving 0.15 + m = -1.456880228 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + m = -1.456880228 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + m = -1.456880228 + -0.15 m = -1.456880228 + -0.15 Combine like terms: -1.456880228 + -0.15 = -1.606880228 m = -1.606880228 Simplifying m = -1.606880228Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.306880228, -1.606880228}
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