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Simplifying 1m2 + 36 = 16m Reorder the terms: 36 + 1m2 = 16m Solving 36 + 1m2 = 16m Solving for variable 'm'. Reorder the terms: 36 + -16m + 1m2 = 16m + -16m Combine like terms: 16m + -16m = 0 36 + -16m + 1m2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -16m + -36 + m2 = 0 + -36 Reorder the terms: 36 + -36 + -16m + m2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -16m + m2 = 0 + -36 -16m + m2 = 0 + -36 Combine like terms: 0 + -36 = -36 -16m + m2 = -36 The m term is -16m. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16m + 64 + m2 = -36 + 64 Reorder the terms: 64 + -16m + m2 = -36 + 64 Combine like terms: -36 + 64 = 28 64 + -16m + m2 = 28 Factor a perfect square on the left side: (m + -8)(m + -8) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (m + -8) equal to 5.291502622 and -5.291502622.Subproblem 1
m + -8 = 5.291502622 Simplifying m + -8 = 5.291502622 Reorder the terms: -8 + m = 5.291502622 Solving -8 + m = 5.291502622 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + m = 5.291502622 + 8 Combine like terms: -8 + 8 = 0 0 + m = 5.291502622 + 8 m = 5.291502622 + 8 Combine like terms: 5.291502622 + 8 = 13.291502622 m = 13.291502622 Simplifying m = 13.291502622Subproblem 2
m + -8 = -5.291502622 Simplifying m + -8 = -5.291502622 Reorder the terms: -8 + m = -5.291502622 Solving -8 + m = -5.291502622 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + m = -5.291502622 + 8 Combine like terms: -8 + 8 = 0 0 + m = -5.291502622 + 8 m = -5.291502622 + 8 Combine like terms: -5.291502622 + 8 = 2.708497378 m = 2.708497378 Simplifying m = 2.708497378Solution
The solution to the problem is based on the solutions from the subproblems. m = {13.291502622, 2.708497378}
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