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Simplifying 7m2 + 24m + -2 = m2 + -9 Reorder the terms: -2 + 24m + 7m2 = m2 + -9 Reorder the terms: -2 + 24m + 7m2 = -9 + m2 Solving -2 + 24m + 7m2 = -9 + m2 Solving for variable 'm'. Reorder the terms: -2 + 9 + 24m + 7m2 + -1m2 = -9 + m2 + 9 + -1m2 Combine like terms: -2 + 9 = 7 7 + 24m + 7m2 + -1m2 = -9 + m2 + 9 + -1m2 Combine like terms: 7m2 + -1m2 = 6m2 7 + 24m + 6m2 = -9 + m2 + 9 + -1m2 Reorder the terms: 7 + 24m + 6m2 = -9 + 9 + m2 + -1m2 Combine like terms: -9 + 9 = 0 7 + 24m + 6m2 = 0 + m2 + -1m2 7 + 24m + 6m2 = m2 + -1m2 Combine like terms: m2 + -1m2 = 0 7 + 24m + 6m2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.166666667 + 4m + m2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + 4m + -1.166666667 + m2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + 4m + m2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + 4m + m2 = 0 + -1.166666667 4m + m2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 4m + m2 = -1.166666667 The m term is 4m. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4m + 4 + m2 = -1.166666667 + 4 Reorder the terms: 4 + 4m + m2 = -1.166666667 + 4 Combine like terms: -1.166666667 + 4 = 2.833333333 4 + 4m + m2 = 2.833333333 Factor a perfect square on the left side: (m + 2)(m + 2) = 2.833333333 Calculate the square root of the right side: 1.683250823 Break this problem into two subproblems by setting (m + 2) equal to 1.683250823 and -1.683250823.Subproblem 1
m + 2 = 1.683250823 Simplifying m + 2 = 1.683250823 Reorder the terms: 2 + m = 1.683250823 Solving 2 + m = 1.683250823 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = 1.683250823 + -2 Combine like terms: 2 + -2 = 0 0 + m = 1.683250823 + -2 m = 1.683250823 + -2 Combine like terms: 1.683250823 + -2 = -0.316749177 m = -0.316749177 Simplifying m = -0.316749177Subproblem 2
m + 2 = -1.683250823 Simplifying m + 2 = -1.683250823 Reorder the terms: 2 + m = -1.683250823 Solving 2 + m = -1.683250823 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = -1.683250823 + -2 Combine like terms: 2 + -2 = 0 0 + m = -1.683250823 + -2 m = -1.683250823 + -2 Combine like terms: -1.683250823 + -2 = -3.683250823 m = -3.683250823 Simplifying m = -3.683250823Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.316749177, -3.683250823}
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