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Simplifying 5m2 + 5m + -21 = 0 Reorder the terms: -21 + 5m + 5m2 = 0 Solving -21 + 5m + 5m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + m + m2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + m + 4.2 + m2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + m + m2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + m + m2 = 0 + 4.2 m + m2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 m + m2 = 4.2 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + m2 = 4.2 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + m2 = 4.2 + 0.25 Combine like terms: 4.2 + 0.25 = 4.45 1.25 + m2 = 4.45 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 4.45 Calculate the square root of the right side: 2.109502311 Break this problem into two subproblems by setting (m + 0.5) equal to 2.109502311 and -2.109502311.Subproblem 1
m + 0.5 = 2.109502311 Simplifying m + 0.5 = 2.109502311 Reorder the terms: 0.5 + m = 2.109502311 Solving 0.5 + m = 2.109502311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 2.109502311 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 2.109502311 + -0.5 m = 2.109502311 + -0.5 Combine like terms: 2.109502311 + -0.5 = 1.609502311 m = 1.609502311 Simplifying m = 1.609502311Subproblem 2
m + 0.5 = -2.109502311 Simplifying m + 0.5 = -2.109502311 Reorder the terms: 0.5 + m = -2.109502311 Solving 0.5 + m = -2.109502311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -2.109502311 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -2.109502311 + -0.5 m = -2.109502311 + -0.5 Combine like terms: -2.109502311 + -0.5 = -2.609502311 m = -2.609502311 Simplifying m = -2.609502311Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.609502311, -2.609502311}
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