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Simplifying 4m2 + 18m = 7 Reorder the terms: 18m + 4m2 = 7 Solving 18m + 4m2 = 7 Solving for variable 'm'. Reorder the terms: -7 + 18m + 4m2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 18m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + 4.5m + m2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 4.5m + 1.75 + m2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 4.5m + m2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 4.5m + m2 = 0 + 1.75 4.5m + m2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 4.5m + m2 = 1.75 The m term is 4.5m. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5m + 5.0625 + m2 = 1.75 + 5.0625 Reorder the terms: 5.0625 + 4.5m + m2 = 1.75 + 5.0625 Combine like terms: 1.75 + 5.0625 = 6.8125 5.0625 + 4.5m + m2 = 6.8125 Factor a perfect square on the left side: (m + 2.25)(m + 2.25) = 6.8125 Calculate the square root of the right side: 2.610076627 Break this problem into two subproblems by setting (m + 2.25) equal to 2.610076627 and -2.610076627.Subproblem 1
m + 2.25 = 2.610076627 Simplifying m + 2.25 = 2.610076627 Reorder the terms: 2.25 + m = 2.610076627 Solving 2.25 + m = 2.610076627 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + m = 2.610076627 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + m = 2.610076627 + -2.25 m = 2.610076627 + -2.25 Combine like terms: 2.610076627 + -2.25 = 0.360076627 m = 0.360076627 Simplifying m = 0.360076627Subproblem 2
m + 2.25 = -2.610076627 Simplifying m + 2.25 = -2.610076627 Reorder the terms: 2.25 + m = -2.610076627 Solving 2.25 + m = -2.610076627 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + m = -2.610076627 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + m = -2.610076627 + -2.25 m = -2.610076627 + -2.25 Combine like terms: -2.610076627 + -2.25 = -4.860076627 m = -4.860076627 Simplifying m = -4.860076627Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.360076627, -4.860076627}
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