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Simplifying m2 + -14m = 36 Reorder the terms: -14m + m2 = 36 Solving -14m + m2 = 36 Solving for variable 'm'. Reorder the terms: -36 + -14m + m2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -14m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -14m + 36 + m2 = 0 + 36 Reorder the terms: -36 + 36 + -14m + m2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -14m + m2 = 0 + 36 -14m + m2 = 0 + 36 Combine like terms: 0 + 36 = 36 -14m + m2 = 36 The m term is -14m. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14m + 49 + m2 = 36 + 49 Reorder the terms: 49 + -14m + m2 = 36 + 49 Combine like terms: 36 + 49 = 85 49 + -14m + m2 = 85 Factor a perfect square on the left side: (m + -7)(m + -7) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (m + -7) equal to 9.219544457 and -9.219544457.Subproblem 1
m + -7 = 9.219544457 Simplifying m + -7 = 9.219544457 Reorder the terms: -7 + m = 9.219544457 Solving -7 + m = 9.219544457 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + m = 9.219544457 + 7 Combine like terms: -7 + 7 = 0 0 + m = 9.219544457 + 7 m = 9.219544457 + 7 Combine like terms: 9.219544457 + 7 = 16.219544457 m = 16.219544457 Simplifying m = 16.219544457Subproblem 2
m + -7 = -9.219544457 Simplifying m + -7 = -9.219544457 Reorder the terms: -7 + m = -9.219544457 Solving -7 + m = -9.219544457 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + m = -9.219544457 + 7 Combine like terms: -7 + 7 = 0 0 + m = -9.219544457 + 7 m = -9.219544457 + 7 Combine like terms: -9.219544457 + 7 = -2.219544457 m = -2.219544457 Simplifying m = -2.219544457Solution
The solution to the problem is based on the solutions from the subproblems. m = {16.219544457, -2.219544457}
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