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Simplifying 7m = -324 + m2 Solving 7m = -324 + m2 Solving for variable 'm'. Reorder the terms: 324 + 7m + -1m2 = -324 + m2 + 324 + -1m2 Reorder the terms: 324 + 7m + -1m2 = -324 + 324 + m2 + -1m2 Combine like terms: -324 + 324 = 0 324 + 7m + -1m2 = 0 + m2 + -1m2 324 + 7m + -1m2 = m2 + -1m2 Combine like terms: m2 + -1m2 = 0 324 + 7m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -324 + -7m + m2 = 0 Move the constant term to the right: Add '324' to each side of the equation. -324 + -7m + 324 + m2 = 0 + 324 Reorder the terms: -324 + 324 + -7m + m2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + -7m + m2 = 0 + 324 -7m + m2 = 0 + 324 Combine like terms: 0 + 324 = 324 -7m + m2 = 324 The m term is -7m. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7m + 12.25 + m2 = 324 + 12.25 Reorder the terms: 12.25 + -7m + m2 = 324 + 12.25 Combine like terms: 324 + 12.25 = 336.25 12.25 + -7m + m2 = 336.25 Factor a perfect square on the left side: (m + -3.5)(m + -3.5) = 336.25 Calculate the square root of the right side: 18.337120821 Break this problem into two subproblems by setting (m + -3.5) equal to 18.337120821 and -18.337120821.Subproblem 1
m + -3.5 = 18.337120821 Simplifying m + -3.5 = 18.337120821 Reorder the terms: -3.5 + m = 18.337120821 Solving -3.5 + m = 18.337120821 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + m = 18.337120821 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + m = 18.337120821 + 3.5 m = 18.337120821 + 3.5 Combine like terms: 18.337120821 + 3.5 = 21.837120821 m = 21.837120821 Simplifying m = 21.837120821Subproblem 2
m + -3.5 = -18.337120821 Simplifying m + -3.5 = -18.337120821 Reorder the terms: -3.5 + m = -18.337120821 Solving -3.5 + m = -18.337120821 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + m = -18.337120821 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + m = -18.337120821 + 3.5 m = -18.337120821 + 3.5 Combine like terms: -18.337120821 + 3.5 = -14.837120821 m = -14.837120821 Simplifying m = -14.837120821Solution
The solution to the problem is based on the solutions from the subproblems. m = {21.837120821, -14.837120821}
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