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Simplifying m2 + -8m + -36 = 4 Reorder the terms: -36 + -8m + m2 = 4 Solving -36 + -8m + m2 = 4 Solving for variable 'm'. Reorder the terms: -36 + -4 + -8m + m2 = 4 + -4 Combine like terms: -36 + -4 = -40 -40 + -8m + m2 = 4 + -4 Combine like terms: 4 + -4 = 0 -40 + -8m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -8m + 40 + m2 = 0 + 40 Reorder the terms: -40 + 40 + -8m + m2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -8m + m2 = 0 + 40 -8m + m2 = 0 + 40 Combine like terms: 0 + 40 = 40 -8m + m2 = 40 The m term is -8m. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8m + 16 + m2 = 40 + 16 Reorder the terms: 16 + -8m + m2 = 40 + 16 Combine like terms: 40 + 16 = 56 16 + -8m + m2 = 56 Factor a perfect square on the left side: (m + -4)(m + -4) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (m + -4) equal to 7.483314774 and -7.483314774.Subproblem 1
m + -4 = 7.483314774 Simplifying m + -4 = 7.483314774 Reorder the terms: -4 + m = 7.483314774 Solving -4 + m = 7.483314774 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = 7.483314774 + 4 Combine like terms: -4 + 4 = 0 0 + m = 7.483314774 + 4 m = 7.483314774 + 4 Combine like terms: 7.483314774 + 4 = 11.483314774 m = 11.483314774 Simplifying m = 11.483314774Subproblem 2
m + -4 = -7.483314774 Simplifying m + -4 = -7.483314774 Reorder the terms: -4 + m = -7.483314774 Solving -4 + m = -7.483314774 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = -7.483314774 + 4 Combine like terms: -4 + 4 = 0 0 + m = -7.483314774 + 4 m = -7.483314774 + 4 Combine like terms: -7.483314774 + 4 = -3.483314774 m = -3.483314774 Simplifying m = -3.483314774Solution
The solution to the problem is based on the solutions from the subproblems. m = {11.483314774, -3.483314774}
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