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Simplifying (5m2 + -5m + 7) + -1(3m2 + -2m + 10) = 0 Reorder the terms: (7 + -5m + 5m2) + -1(3m2 + -2m + 10) = 0 Remove parenthesis around (7 + -5m + 5m2) 7 + -5m + 5m2 + -1(3m2 + -2m + 10) = 0 Reorder the terms: 7 + -5m + 5m2 + -1(10 + -2m + 3m2) = 0 7 + -5m + 5m2 + (10 * -1 + -2m * -1 + 3m2 * -1) = 0 7 + -5m + 5m2 + (-10 + 2m + -3m2) = 0 Reorder the terms: 7 + -10 + -5m + 2m + 5m2 + -3m2 = 0 Combine like terms: 7 + -10 = -3 -3 + -5m + 2m + 5m2 + -3m2 = 0 Combine like terms: -5m + 2m = -3m -3 + -3m + 5m2 + -3m2 = 0 Combine like terms: 5m2 + -3m2 = 2m2 -3 + -3m + 2m2 = 0 Solving -3 + -3m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -1.5m + m2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -1.5m + 1.5 + m2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -1.5m + m2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1.5m + m2 = 0 + 1.5 -1.5m + m2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -1.5m + m2 = 1.5 The m term is -1.5m. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5m + 0.5625 + m2 = 1.5 + 0.5625 Reorder the terms: 0.5625 + -1.5m + m2 = 1.5 + 0.5625 Combine like terms: 1.5 + 0.5625 = 2.0625 0.5625 + -1.5m + m2 = 2.0625 Factor a perfect square on the left side: (m + -0.75)(m + -0.75) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (m + -0.75) equal to 1.436140662 and -1.436140662.Subproblem 1
m + -0.75 = 1.436140662 Simplifying m + -0.75 = 1.436140662 Reorder the terms: -0.75 + m = 1.436140662 Solving -0.75 + m = 1.436140662 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + m = 1.436140662 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = 1.436140662 + 0.75 m = 1.436140662 + 0.75 Combine like terms: 1.436140662 + 0.75 = 2.186140662 m = 2.186140662 Simplifying m = 2.186140662Subproblem 2
m + -0.75 = -1.436140662 Simplifying m + -0.75 = -1.436140662 Reorder the terms: -0.75 + m = -1.436140662 Solving -0.75 + m = -1.436140662 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + m = -1.436140662 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = -1.436140662 + 0.75 m = -1.436140662 + 0.75 Combine like terms: -1.436140662 + 0.75 = -0.686140662 m = -0.686140662 Simplifying m = -0.686140662Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.186140662, -0.686140662}
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