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Simplifying 5m2 + 16m + 5 = 0 Reorder the terms: 5 + 16m + 5m2 = 0 Solving 5 + 16m + 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'. 1 + 3.2m + m2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 3.2m + -1 + m2 = 0 + -1 Reorder the terms: 1 + -1 + 3.2m + m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3.2m + m2 = 0 + -1 3.2m + m2 = 0 + -1 Combine like terms: 0 + -1 = -1 3.2m + m2 = -1 The m term is 3.2m. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2m + 2.56 + m2 = -1 + 2.56 Reorder the terms: 2.56 + 3.2m + m2 = -1 + 2.56 Combine like terms: -1 + 2.56 = 1.56 2.56 + 3.2m + m2 = 1.56 Factor a perfect square on the left side: (m + 1.6)(m + 1.6) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (m + 1.6) equal to 1.2489996 and -1.2489996.Subproblem 1
m + 1.6 = 1.2489996 Simplifying m + 1.6 = 1.2489996 Reorder the terms: 1.6 + m = 1.2489996 Solving 1.6 + m = 1.2489996 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + m = 1.2489996 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + m = 1.2489996 + -1.6 m = 1.2489996 + -1.6 Combine like terms: 1.2489996 + -1.6 = -0.3510004 m = -0.3510004 Simplifying m = -0.3510004Subproblem 2
m + 1.6 = -1.2489996 Simplifying m + 1.6 = -1.2489996 Reorder the terms: 1.6 + m = -1.2489996 Solving 1.6 + m = -1.2489996 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + m = -1.2489996 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + m = -1.2489996 + -1.6 m = -1.2489996 + -1.6 Combine like terms: -1.2489996 + -1.6 = -2.8489996 m = -2.8489996 Simplifying m = -2.8489996Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.3510004, -2.8489996}
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