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Simplifying 5m2 = 17 + -4m Solving 5m2 = 17 + -4m Solving for variable 'm'. Reorder the terms: -17 + 4m + 5m2 = 17 + -4m + -17 + 4m Reorder the terms: -17 + 4m + 5m2 = 17 + -17 + -4m + 4m Combine like terms: 17 + -17 = 0 -17 + 4m + 5m2 = 0 + -4m + 4m -17 + 4m + 5m2 = -4m + 4m Combine like terms: -4m + 4m = 0 -17 + 4m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.4 + 0.8m + m2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + 0.8m + 3.4 + m2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + 0.8m + m2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + 0.8m + m2 = 0 + 3.4 0.8m + m2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 0.8m + m2 = 3.4 The m term is 0.8m. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8m + 0.16 + m2 = 3.4 + 0.16 Reorder the terms: 0.16 + 0.8m + m2 = 3.4 + 0.16 Combine like terms: 3.4 + 0.16 = 3.56 0.16 + 0.8m + m2 = 3.56 Factor a perfect square on the left side: (m + 0.4)(m + 0.4) = 3.56 Calculate the square root of the right side: 1.886796226 Break this problem into two subproblems by setting (m + 0.4) equal to 1.886796226 and -1.886796226.Subproblem 1
m + 0.4 = 1.886796226 Simplifying m + 0.4 = 1.886796226 Reorder the terms: 0.4 + m = 1.886796226 Solving 0.4 + m = 1.886796226 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + m = 1.886796226 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + m = 1.886796226 + -0.4 m = 1.886796226 + -0.4 Combine like terms: 1.886796226 + -0.4 = 1.486796226 m = 1.486796226 Simplifying m = 1.486796226Subproblem 2
m + 0.4 = -1.886796226 Simplifying m + 0.4 = -1.886796226 Reorder the terms: 0.4 + m = -1.886796226 Solving 0.4 + m = -1.886796226 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + m = -1.886796226 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + m = -1.886796226 + -0.4 m = -1.886796226 + -0.4 Combine like terms: -1.886796226 + -0.4 = -2.286796226 m = -2.286796226 Simplifying m = -2.286796226Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.486796226, -2.286796226}
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