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Simplifying m2 + 24m + -34 = 32 Reorder the terms: -34 + 24m + m2 = 32 Solving -34 + 24m + m2 = 32 Solving for variable 'm'. Reorder the terms: -34 + -32 + 24m + m2 = 32 + -32 Combine like terms: -34 + -32 = -66 -66 + 24m + m2 = 32 + -32 Combine like terms: 32 + -32 = 0 -66 + 24m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + 24m + 66 + m2 = 0 + 66 Reorder the terms: -66 + 66 + 24m + m2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 24m + m2 = 0 + 66 24m + m2 = 0 + 66 Combine like terms: 0 + 66 = 66 24m + m2 = 66 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 = 66 + 144 Reorder the terms: 144 + 24m + m2 = 66 + 144 Combine like terms: 66 + 144 = 210 144 + 24m + m2 = 210 Factor a perfect square on the left side: (m + 12)(m + 12) = 210 Calculate the square root of the right side: 14.491376746 Break this problem into two subproblems by setting (m + 12) equal to 14.491376746 and -14.491376746.Subproblem 1
m + 12 = 14.491376746 Simplifying m + 12 = 14.491376746 Reorder the terms: 12 + m = 14.491376746 Solving 12 + m = 14.491376746 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 = 14.491376746 + -12 Combine like terms: 12 + -12 = 0 0 + m = 14.491376746 + -12 m = 14.491376746 + -12 Combine like terms: 14.491376746 + -12 = 2.491376746 m = 2.491376746 Simplifying m = 2.491376746Subproblem 2
m + 12 = -14.491376746 Simplifying m + 12 = -14.491376746 Reorder the terms: 12 + m = -14.491376746 Solving 12 + m = -14.491376746 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 = -14.491376746 + -12 Combine like terms: 12 + -12 = 0 0 + m = -14.491376746 + -12 m = -14.491376746 + -12 Combine like terms: -14.491376746 + -12 = -26.491376746 m = -26.491376746 Simplifying m = -26.491376746Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.491376746, -26.491376746}
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