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Simplifying m2 + -4m + -51 = 0 Reorder the terms: -51 + -4m + m2 = 0 Solving -51 + -4m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + -4m + 51 + m2 = 0 + 51 Reorder the terms: -51 + 51 + -4m + m2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + -4m + m2 = 0 + 51 -4m + m2 = 0 + 51 Combine like terms: 0 + 51 = 51 -4m + m2 = 51 The m term is -4m. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m + 4 + m2 = 51 + 4 Reorder the terms: 4 + -4m + m2 = 51 + 4 Combine like terms: 51 + 4 = 55 4 + -4m + m2 = 55 Factor a perfect square on the left side: (m + -2)(m + -2) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (m + -2) equal to 7.416198487 and -7.416198487.Subproblem 1
m + -2 = 7.416198487 Simplifying m + -2 = 7.416198487 Reorder the terms: -2 + m = 7.416198487 Solving -2 + m = 7.416198487 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = 7.416198487 + 2 Combine like terms: -2 + 2 = 0 0 + m = 7.416198487 + 2 m = 7.416198487 + 2 Combine like terms: 7.416198487 + 2 = 9.416198487 m = 9.416198487 Simplifying m = 9.416198487Subproblem 2
m + -2 = -7.416198487 Simplifying m + -2 = -7.416198487 Reorder the terms: -2 + m = -7.416198487 Solving -2 + m = -7.416198487 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = -7.416198487 + 2 Combine like terms: -2 + 2 = 0 0 + m = -7.416198487 + 2 m = -7.416198487 + 2 Combine like terms: -7.416198487 + 2 = -5.416198487 m = -5.416198487 Simplifying m = -5.416198487Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.416198487, -5.416198487}
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