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Simplifying (5m + -6)(5m + -6) = 7 Reorder the terms: (-6 + 5m)(5m + -6) = 7 Reorder the terms: (-6 + 5m)(-6 + 5m) = 7 Multiply (-6 + 5m) * (-6 + 5m) (-6(-6 + 5m) + 5m * (-6 + 5m)) = 7 ((-6 * -6 + 5m * -6) + 5m * (-6 + 5m)) = 7 ((36 + -30m) + 5m * (-6 + 5m)) = 7 (36 + -30m + (-6 * 5m + 5m * 5m)) = 7 (36 + -30m + (-30m + 25m2)) = 7 Combine like terms: -30m + -30m = -60m (36 + -60m + 25m2) = 7 Solving 36 + -60m + 25m2 = 7 Solving for variable 'm'. Reorder the terms: 36 + -7 + -60m + 25m2 = 7 + -7 Combine like terms: 36 + -7 = 29 29 + -60m + 25m2 = 7 + -7 Combine like terms: 7 + -7 = 0 29 + -60m + 25m2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 1.16 + -2.4m + m2 = 0 Move the constant term to the right: Add '-1.16' to each side of the equation. 1.16 + -2.4m + -1.16 + m2 = 0 + -1.16 Reorder the terms: 1.16 + -1.16 + -2.4m + m2 = 0 + -1.16 Combine like terms: 1.16 + -1.16 = 0.00 0.00 + -2.4m + m2 = 0 + -1.16 -2.4m + m2 = 0 + -1.16 Combine like terms: 0 + -1.16 = -1.16 -2.4m + m2 = -1.16 The m term is -2.4m. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4m + 1.44 + m2 = -1.16 + 1.44 Reorder the terms: 1.44 + -2.4m + m2 = -1.16 + 1.44 Combine like terms: -1.16 + 1.44 = 0.28 1.44 + -2.4m + m2 = 0.28 Factor a perfect square on the left side: (m + -1.2)(m + -1.2) = 0.28 Calculate the square root of the right side: 0.529150262 Break this problem into two subproblems by setting (m + -1.2) equal to 0.529150262 and -0.529150262.Subproblem 1
m + -1.2 = 0.529150262 Simplifying m + -1.2 = 0.529150262 Reorder the terms: -1.2 + m = 0.529150262 Solving -1.2 + m = 0.529150262 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + m = 0.529150262 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + m = 0.529150262 + 1.2 m = 0.529150262 + 1.2 Combine like terms: 0.529150262 + 1.2 = 1.729150262 m = 1.729150262 Simplifying m = 1.729150262Subproblem 2
m + -1.2 = -0.529150262 Simplifying m + -1.2 = -0.529150262 Reorder the terms: -1.2 + m = -0.529150262 Solving -1.2 + m = -0.529150262 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + m = -0.529150262 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + m = -0.529150262 + 1.2 m = -0.529150262 + 1.2 Combine like terms: -0.529150262 + 1.2 = 0.670849738 m = 0.670849738 Simplifying m = 0.670849738Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.729150262, 0.670849738}
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