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Simplifying 4m = (m + 4)(2 + -1m) Reorder the terms: 4m = (4 + m)(2 + -1m) Multiply (4 + m) * (2 + -1m) 4m = (4(2 + -1m) + m(2 + -1m)) 4m = ((2 * 4 + -1m * 4) + m(2 + -1m)) 4m = ((8 + -4m) + m(2 + -1m)) 4m = (8 + -4m + (2 * m + -1m * m)) 4m = (8 + -4m + (2m + -1m2)) Combine like terms: -4m + 2m = -2m 4m = (8 + -2m + -1m2) Solving 4m = 8 + -2m + -1m2 Solving for variable 'm'. Reorder the terms: -8 + 4m + 2m + m2 = 8 + -2m + -1m2 + -8 + 2m + m2 Combine like terms: 4m + 2m = 6m -8 + 6m + m2 = 8 + -2m + -1m2 + -8 + 2m + m2 Reorder the terms: -8 + 6m + m2 = 8 + -8 + -2m + 2m + -1m2 + m2 Combine like terms: 8 + -8 = 0 -8 + 6m + m2 = 0 + -2m + 2m + -1m2 + m2 -8 + 6m + m2 = -2m + 2m + -1m2 + m2 Combine like terms: -2m + 2m = 0 -8 + 6m + m2 = 0 + -1m2 + m2 -8 + 6m + m2 = -1m2 + m2 Combine like terms: -1m2 + m2 = 0 -8 + 6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 6m + 8 + m2 = 0 + 8 Reorder the terms: -8 + 8 + 6m + m2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 6m + m2 = 0 + 8 6m + m2 = 0 + 8 Combine like terms: 0 + 8 = 8 6m + m2 = 8 The m term is 6m. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6m + 9 + m2 = 8 + 9 Reorder the terms: 9 + 6m + m2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + 6m + m2 = 17 Factor a perfect square on the left side: (m + 3)(m + 3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (m + 3) equal to 4.123105626 and -4.123105626.Subproblem 1
m + 3 = 4.123105626 Simplifying m + 3 = 4.123105626 Reorder the terms: 3 + m = 4.123105626 Solving 3 + m = 4.123105626 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = 4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + m = 4.123105626 + -3 m = 4.123105626 + -3 Combine like terms: 4.123105626 + -3 = 1.123105626 m = 1.123105626 Simplifying m = 1.123105626Subproblem 2
m + 3 = -4.123105626 Simplifying m + 3 = -4.123105626 Reorder the terms: 3 + m = -4.123105626 Solving 3 + m = -4.123105626 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = -4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + m = -4.123105626 + -3 m = -4.123105626 + -3 Combine like terms: -4.123105626 + -3 = -7.123105626 m = -7.123105626 Simplifying m = -7.123105626Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.123105626, -7.123105626}
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