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Simplifying 8m2 + -16m = 65 Reorder the terms: -16m + 8m2 = 65 Solving -16m + 8m2 = 65 Solving for variable 'm'. Reorder the terms: -65 + -16m + 8m2 = 65 + -65 Combine like terms: 65 + -65 = 0 -65 + -16m + 8m2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -8.125 + -2m + m2 = 0 Move the constant term to the right: Add '8.125' to each side of the equation. -8.125 + -2m + 8.125 + m2 = 0 + 8.125 Reorder the terms: -8.125 + 8.125 + -2m + m2 = 0 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + -2m + m2 = 0 + 8.125 -2m + m2 = 0 + 8.125 Combine like terms: 0 + 8.125 = 8.125 -2m + m2 = 8.125 The m term is -2m. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2m + 1 + m2 = 8.125 + 1 Reorder the terms: 1 + -2m + m2 = 8.125 + 1 Combine like terms: 8.125 + 1 = 9.125 1 + -2m + m2 = 9.125 Factor a perfect square on the left side: (m + -1)(m + -1) = 9.125 Calculate the square root of the right side: 3.020761493 Break this problem into two subproblems by setting (m + -1) equal to 3.020761493 and -3.020761493.Subproblem 1
m + -1 = 3.020761493 Simplifying m + -1 = 3.020761493 Reorder the terms: -1 + m = 3.020761493 Solving -1 + m = 3.020761493 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 3.020761493 + 1 Combine like terms: -1 + 1 = 0 0 + m = 3.020761493 + 1 m = 3.020761493 + 1 Combine like terms: 3.020761493 + 1 = 4.020761493 m = 4.020761493 Simplifying m = 4.020761493Subproblem 2
m + -1 = -3.020761493 Simplifying m + -1 = -3.020761493 Reorder the terms: -1 + m = -3.020761493 Solving -1 + m = -3.020761493 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -3.020761493 + 1 Combine like terms: -1 + 1 = 0 0 + m = -3.020761493 + 1 m = -3.020761493 + 1 Combine like terms: -3.020761493 + 1 = -2.020761493 m = -2.020761493 Simplifying m = -2.020761493Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.020761493, -2.020761493}
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