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Simplifying 15 = m2 + -14m + 49 Reorder the terms: 15 = 49 + -14m + m2 Solving 15 = 49 + -14m + m2 Solving for variable 'm'. Combine like terms: 15 + -49 = -34 -34 + 14m + -1m2 = 49 + -14m + m2 + -49 + 14m + -1m2 Reorder the terms: -34 + 14m + -1m2 = 49 + -49 + -14m + 14m + m2 + -1m2 Combine like terms: 49 + -49 = 0 -34 + 14m + -1m2 = 0 + -14m + 14m + m2 + -1m2 -34 + 14m + -1m2 = -14m + 14m + m2 + -1m2 Combine like terms: -14m + 14m = 0 -34 + 14m + -1m2 = 0 + m2 + -1m2 -34 + 14m + -1m2 = m2 + -1m2 Combine like terms: m2 + -1m2 = 0 -34 + 14m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 34 + -14m + m2 = 0 Move the constant term to the right: Add '-34' to each side of the equation. 34 + -14m + -34 + m2 = 0 + -34 Reorder the terms: 34 + -34 + -14m + m2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -14m + m2 = 0 + -34 -14m + m2 = 0 + -34 Combine like terms: 0 + -34 = -34 -14m + m2 = -34 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 = -34 + 49 Reorder the terms: 49 + -14m + m2 = -34 + 49 Combine like terms: -34 + 49 = 15 49 + -14m + m2 = 15 Factor a perfect square on the left side: (m + -7)(m + -7) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (m + -7) equal to 3.872983346 and -3.872983346.Subproblem 1
m + -7 = 3.872983346 Simplifying m + -7 = 3.872983346 Reorder the terms: -7 + m = 3.872983346 Solving -7 + m = 3.872983346 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 = 3.872983346 + 7 Combine like terms: -7 + 7 = 0 0 + m = 3.872983346 + 7 m = 3.872983346 + 7 Combine like terms: 3.872983346 + 7 = 10.872983346 m = 10.872983346 Simplifying m = 10.872983346Subproblem 2
m + -7 = -3.872983346 Simplifying m + -7 = -3.872983346 Reorder the terms: -7 + m = -3.872983346 Solving -7 + m = -3.872983346 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 = -3.872983346 + 7 Combine like terms: -7 + 7 = 0 0 + m = -3.872983346 + 7 m = -3.872983346 + 7 Combine like terms: -3.872983346 + 7 = 3.127016654 m = 3.127016654 Simplifying m = 3.127016654Solution
The solution to the problem is based on the solutions from the subproblems. m = {10.872983346, 3.127016654}
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