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Simplifying m + 5m2 + -6 = 10 Reorder the terms: -6 + m + 5m2 = 10 Solving -6 + m + 5m2 = 10 Solving for variable 'm'. Reorder the terms: -6 + -10 + m + 5m2 = 10 + -10 Combine like terms: -6 + -10 = -16 -16 + m + 5m2 = 10 + -10 Combine like terms: 10 + -10 = 0 -16 + m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + 0.2m + m2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 0.2m + 3.2 + m2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 0.2m + m2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 0.2m + m2 = 0 + 3.2 0.2m + m2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 0.2m + m2 = 3.2 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. 0.2m + 0.25 + m2 = 3.2 + 0.25 Reorder the terms: 0.25 + 0.2m + m2 = 3.2 + 0.25 Combine like terms: 3.2 + 0.25 = 3.45 0.25 + 0.2m + m2 = 3.45 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 3.45 Calculate the square root of the right side: 1.857417562 Break this problem into two subproblems by setting (m + 0.5) equal to 1.857417562 and -1.857417562.Subproblem 1
m + 0.5 = 1.857417562 Simplifying m + 0.5 = 1.857417562 Reorder the terms: 0.5 + m = 1.857417562 Solving 0.5 + m = 1.857417562 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 = 1.857417562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 1.857417562 + -0.5 m = 1.857417562 + -0.5 Combine like terms: 1.857417562 + -0.5 = 1.357417562 m = 1.357417562 Simplifying m = 1.357417562Subproblem 2
m + 0.5 = -1.857417562 Simplifying m + 0.5 = -1.857417562 Reorder the terms: 0.5 + m = -1.857417562 Solving 0.5 + m = -1.857417562 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 = -1.857417562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -1.857417562 + -0.5 m = -1.857417562 + -0.5 Combine like terms: -1.857417562 + -0.5 = -2.357417562 m = -2.357417562 Simplifying m = -2.357417562Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.357417562, -2.357417562}
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