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Simplifying 5m + 2m(m + -5) = 17 Reorder the terms: 5m + 2m(-5 + m) = 17 5m + (-5 * 2m + m * 2m) = 17 5m + (-10m + 2m2) = 17 Combine like terms: 5m + -10m = -5m -5m + 2m2 = 17 Solving -5m + 2m2 = 17 Solving for variable 'm'. Reorder the terms: -17 + -5m + 2m2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -5m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.5 + -2.5m + m2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -2.5m + 8.5 + m2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -2.5m + m2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -2.5m + m2 = 0 + 8.5 -2.5m + m2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -2.5m + m2 = 8.5 The m term is -2.5m. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5m + 1.5625 + m2 = 8.5 + 1.5625 Reorder the terms: 1.5625 + -2.5m + m2 = 8.5 + 1.5625 Combine like terms: 8.5 + 1.5625 = 10.0625 1.5625 + -2.5m + m2 = 10.0625 Factor a perfect square on the left side: (m + -1.25)(m + -1.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (m + -1.25) equal to 3.172144385 and -3.172144385.Subproblem 1
m + -1.25 = 3.172144385 Simplifying m + -1.25 = 3.172144385 Reorder the terms: -1.25 + m = 3.172144385 Solving -1.25 + m = 3.172144385 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + m = 3.172144385 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + m = 3.172144385 + 1.25 m = 3.172144385 + 1.25 Combine like terms: 3.172144385 + 1.25 = 4.422144385 m = 4.422144385 Simplifying m = 4.422144385Subproblem 2
m + -1.25 = -3.172144385 Simplifying m + -1.25 = -3.172144385 Reorder the terms: -1.25 + m = -3.172144385 Solving -1.25 + m = -3.172144385 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + m = -3.172144385 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + m = -3.172144385 + 1.25 m = -3.172144385 + 1.25 Combine like terms: -3.172144385 + 1.25 = -1.922144385 m = -1.922144385 Simplifying m = -1.922144385Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.422144385, -1.922144385}
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