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Simplifying m2 + 12m = 49 Reorder the terms: 12m + m2 = 49 Solving 12m + m2 = 49 Solving for variable 'm'. Reorder the terms: -49 + 12m + m2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + 12m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 12m + 49 + m2 = 0 + 49 Reorder the terms: -49 + 49 + 12m + m2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 12m + m2 = 0 + 49 12m + m2 = 0 + 49 Combine like terms: 0 + 49 = 49 12m + m2 = 49 The m term is 12m. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12m + 36 + m2 = 49 + 36 Reorder the terms: 36 + 12m + m2 = 49 + 36 Combine like terms: 49 + 36 = 85 36 + 12m + m2 = 85 Factor a perfect square on the left side: (m + 6)(m + 6) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (m + 6) equal to 9.219544457 and -9.219544457.Subproblem 1
m + 6 = 9.219544457 Simplifying m + 6 = 9.219544457 Reorder the terms: 6 + m = 9.219544457 Solving 6 + m = 9.219544457 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + m = 9.219544457 + -6 Combine like terms: 6 + -6 = 0 0 + m = 9.219544457 + -6 m = 9.219544457 + -6 Combine like terms: 9.219544457 + -6 = 3.219544457 m = 3.219544457 Simplifying m = 3.219544457Subproblem 2
m + 6 = -9.219544457 Simplifying m + 6 = -9.219544457 Reorder the terms: 6 + m = -9.219544457 Solving 6 + m = -9.219544457 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + m = -9.219544457 + -6 Combine like terms: 6 + -6 = 0 0 + m = -9.219544457 + -6 m = -9.219544457 + -6 Combine like terms: -9.219544457 + -6 = -15.219544457 m = -15.219544457 Simplifying m = -15.219544457Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.219544457, -15.219544457}
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