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Simplifying m2 + -24m + 9 = 0 Reorder the terms: 9 + -24m + m2 = 0 Solving 9 + -24m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -24m + -9 + m2 = 0 + -9 Reorder the terms: 9 + -9 + -24m + m2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -24m + m2 = 0 + -9 -24m + m2 = 0 + -9 Combine like terms: 0 + -9 = -9 -24m + m2 = -9 The m term is -24m. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24m + 144 + m2 = -9 + 144 Reorder the terms: 144 + -24m + m2 = -9 + 144 Combine like terms: -9 + 144 = 135 144 + -24m + m2 = 135 Factor a perfect square on the left side: (m + -12)(m + -12) = 135 Calculate the square root of the right side: 11.618950039 Break this problem into two subproblems by setting (m + -12) equal to 11.618950039 and -11.618950039.Subproblem 1
m + -12 = 11.618950039 Simplifying m + -12 = 11.618950039 Reorder the terms: -12 + m = 11.618950039 Solving -12 + m = 11.618950039 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + m = 11.618950039 + 12 Combine like terms: -12 + 12 = 0 0 + m = 11.618950039 + 12 m = 11.618950039 + 12 Combine like terms: 11.618950039 + 12 = 23.618950039 m = 23.618950039 Simplifying m = 23.618950039Subproblem 2
m + -12 = -11.618950039 Simplifying m + -12 = -11.618950039 Reorder the terms: -12 + m = -11.618950039 Solving -12 + m = -11.618950039 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + m = -11.618950039 + 12 Combine like terms: -12 + 12 = 0 0 + m = -11.618950039 + 12 m = -11.618950039 + 12 Combine like terms: -11.618950039 + 12 = 0.381049961 m = 0.381049961 Simplifying m = 0.381049961Solution
The solution to the problem is based on the solutions from the subproblems. m = {23.618950039, 0.381049961}
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