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Simplifying (m + 10)(m + -4) = 8 Reorder the terms: (10 + m)(m + -4) = 8 Reorder the terms: (10 + m)(-4 + m) = 8 Multiply (10 + m) * (-4 + m) (10(-4 + m) + m(-4 + m)) = 8 ((-4 * 10 + m * 10) + m(-4 + m)) = 8 ((-40 + 10m) + m(-4 + m)) = 8 (-40 + 10m + (-4 * m + m * m)) = 8 (-40 + 10m + (-4m + m2)) = 8 Combine like terms: 10m + -4m = 6m (-40 + 6m + m2) = 8 Solving -40 + 6m + m2 = 8 Solving for variable 'm'. Reorder the terms: -40 + -8 + 6m + m2 = 8 + -8 Combine like terms: -40 + -8 = -48 -48 + 6m + m2 = 8 + -8 Combine like terms: 8 + -8 = 0 -48 + 6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 6m + 48 + m2 = 0 + 48 Reorder the terms: -48 + 48 + 6m + m2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 6m + m2 = 0 + 48 6m + m2 = 0 + 48 Combine like terms: 0 + 48 = 48 6m + m2 = 48 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 = 48 + 9 Reorder the terms: 9 + 6m + m2 = 48 + 9 Combine like terms: 48 + 9 = 57 9 + 6m + m2 = 57 Factor a perfect square on the left side: (m + 3)(m + 3) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (m + 3) equal to 7.549834435 and -7.549834435.Subproblem 1
m + 3 = 7.549834435 Simplifying m + 3 = 7.549834435 Reorder the terms: 3 + m = 7.549834435 Solving 3 + m = 7.549834435 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 = 7.549834435 + -3 Combine like terms: 3 + -3 = 0 0 + m = 7.549834435 + -3 m = 7.549834435 + -3 Combine like terms: 7.549834435 + -3 = 4.549834435 m = 4.549834435 Simplifying m = 4.549834435Subproblem 2
m + 3 = -7.549834435 Simplifying m + 3 = -7.549834435 Reorder the terms: 3 + m = -7.549834435 Solving 3 + m = -7.549834435 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 = -7.549834435 + -3 Combine like terms: 3 + -3 = 0 0 + m = -7.549834435 + -3 m = -7.549834435 + -3 Combine like terms: -7.549834435 + -3 = -10.549834435 m = -10.549834435 Simplifying m = -10.549834435Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.549834435, -10.549834435}
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