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Simplifying m2 + 7m + -65 = 0 Reorder the terms: -65 + 7m + m2 = 0 Solving -65 + 7m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + 7m + 65 + m2 = 0 + 65 Reorder the terms: -65 + 65 + 7m + m2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 7m + m2 = 0 + 65 7m + m2 = 0 + 65 Combine like terms: 0 + 65 = 65 7m + m2 = 65 The m term is 7m. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7m + 12.25 + m2 = 65 + 12.25 Reorder the terms: 12.25 + 7m + m2 = 65 + 12.25 Combine like terms: 65 + 12.25 = 77.25 12.25 + 7m + m2 = 77.25 Factor a perfect square on the left side: (m + 3.5)(m + 3.5) = 77.25 Calculate the square root of the right side: 8.789197916 Break this problem into two subproblems by setting (m + 3.5) equal to 8.789197916 and -8.789197916.Subproblem 1
m + 3.5 = 8.789197916 Simplifying m + 3.5 = 8.789197916 Reorder the terms: 3.5 + m = 8.789197916 Solving 3.5 + m = 8.789197916 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = 8.789197916 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = 8.789197916 + -3.5 m = 8.789197916 + -3.5 Combine like terms: 8.789197916 + -3.5 = 5.289197916 m = 5.289197916 Simplifying m = 5.289197916Subproblem 2
m + 3.5 = -8.789197916 Simplifying m + 3.5 = -8.789197916 Reorder the terms: 3.5 + m = -8.789197916 Solving 3.5 + m = -8.789197916 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = -8.789197916 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = -8.789197916 + -3.5 m = -8.789197916 + -3.5 Combine like terms: -8.789197916 + -3.5 = -12.289197916 m = -12.289197916 Simplifying m = -12.289197916Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.289197916, -12.289197916}
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