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Simplifying 5m(m + -2) = 16 Reorder the terms: 5m(-2 + m) = 16 (-2 * 5m + m * 5m) = 16 (-10m + 5m2) = 16 Solving -10m + 5m2 = 16 Solving for variable 'm'. Reorder the terms: -16 + -10m + 5m2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -10m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + -2m + m2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -2m + 3.2 + m2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -2m + m2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -2m + m2 = 0 + 3.2 -2m + m2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -2m + m2 = 3.2 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 = 3.2 + 1 Reorder the terms: 1 + -2m + m2 = 3.2 + 1 Combine like terms: 3.2 + 1 = 4.2 1 + -2m + m2 = 4.2 Factor a perfect square on the left side: (m + -1)(m + -1) = 4.2 Calculate the square root of the right side: 2.049390153 Break this problem into two subproblems by setting (m + -1) equal to 2.049390153 and -2.049390153.Subproblem 1
m + -1 = 2.049390153 Simplifying m + -1 = 2.049390153 Reorder the terms: -1 + m = 2.049390153 Solving -1 + m = 2.049390153 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 = 2.049390153 + 1 Combine like terms: -1 + 1 = 0 0 + m = 2.049390153 + 1 m = 2.049390153 + 1 Combine like terms: 2.049390153 + 1 = 3.049390153 m = 3.049390153 Simplifying m = 3.049390153Subproblem 2
m + -1 = -2.049390153 Simplifying m + -1 = -2.049390153 Reorder the terms: -1 + m = -2.049390153 Solving -1 + m = -2.049390153 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 = -2.049390153 + 1 Combine like terms: -1 + 1 = 0 0 + m = -2.049390153 + 1 m = -2.049390153 + 1 Combine like terms: -2.049390153 + 1 = -1.049390153 m = -1.049390153 Simplifying m = -1.049390153Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.049390153, -1.049390153}
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