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Simplifying m2 + -14m + -6 = 0 Reorder the terms: -6 + -14m + m2 = 0 Solving -6 + -14m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -14m + 6 + m2 = 0 + 6 Reorder the terms: -6 + 6 + -14m + m2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -14m + m2 = 0 + 6 -14m + m2 = 0 + 6 Combine like terms: 0 + 6 = 6 -14m + m2 = 6 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 = 6 + 49 Reorder the terms: 49 + -14m + m2 = 6 + 49 Combine like terms: 6 + 49 = 55 49 + -14m + m2 = 55 Factor a perfect square on the left side: (m + -7)(m + -7) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (m + -7) equal to 7.416198487 and -7.416198487.Subproblem 1
m + -7 = 7.416198487 Simplifying m + -7 = 7.416198487 Reorder the terms: -7 + m = 7.416198487 Solving -7 + m = 7.416198487 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 = 7.416198487 + 7 Combine like terms: -7 + 7 = 0 0 + m = 7.416198487 + 7 m = 7.416198487 + 7 Combine like terms: 7.416198487 + 7 = 14.416198487 m = 14.416198487 Simplifying m = 14.416198487Subproblem 2
m + -7 = -7.416198487 Simplifying m + -7 = -7.416198487 Reorder the terms: -7 + m = -7.416198487 Solving -7 + m = -7.416198487 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 = -7.416198487 + 7 Combine like terms: -7 + 7 = 0 0 + m = -7.416198487 + 7 m = -7.416198487 + 7 Combine like terms: -7.416198487 + 7 = -0.416198487 m = -0.416198487 Simplifying m = -0.416198487Solution
The solution to the problem is based on the solutions from the subproblems. m = {14.416198487, -0.416198487}
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