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Simplifying m2 = 8m + 13 Reorder the terms: m2 = 13 + 8m Solving m2 = 13 + 8m Solving for variable 'm'. Reorder the terms: -13 + -8m + m2 = 13 + 8m + -13 + -8m Reorder the terms: -13 + -8m + m2 = 13 + -13 + 8m + -8m Combine like terms: 13 + -13 = 0 -13 + -8m + m2 = 0 + 8m + -8m -13 + -8m + m2 = 8m + -8m Combine like terms: 8m + -8m = 0 -13 + -8m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -8m + 13 + m2 = 0 + 13 Reorder the terms: -13 + 13 + -8m + m2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -8m + m2 = 0 + 13 -8m + m2 = 0 + 13 Combine like terms: 0 + 13 = 13 -8m + m2 = 13 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 = 13 + 16 Reorder the terms: 16 + -8m + m2 = 13 + 16 Combine like terms: 13 + 16 = 29 16 + -8m + m2 = 29 Factor a perfect square on the left side: (m + -4)(m + -4) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (m + -4) equal to 5.385164807 and -5.385164807.Subproblem 1
m + -4 = 5.385164807 Simplifying m + -4 = 5.385164807 Reorder the terms: -4 + m = 5.385164807 Solving -4 + m = 5.385164807 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 = 5.385164807 + 4 Combine like terms: -4 + 4 = 0 0 + m = 5.385164807 + 4 m = 5.385164807 + 4 Combine like terms: 5.385164807 + 4 = 9.385164807 m = 9.385164807 Simplifying m = 9.385164807Subproblem 2
m + -4 = -5.385164807 Simplifying m + -4 = -5.385164807 Reorder the terms: -4 + m = -5.385164807 Solving -4 + m = -5.385164807 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 = -5.385164807 + 4 Combine like terms: -4 + 4 = 0 0 + m = -5.385164807 + 4 m = -5.385164807 + 4 Combine like terms: -5.385164807 + 4 = -1.385164807 m = -1.385164807 Simplifying m = -1.385164807Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.385164807, -1.385164807}
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