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Simplifying 2m2 + 11m + -14 = 0 Reorder the terms: -14 + 11m + 2m2 = 0 Solving -14 + 11m + 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'. -7 + 5.5m + m2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 5.5m + 7 + m2 = 0 + 7 Reorder the terms: -7 + 7 + 5.5m + m2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 5.5m + m2 = 0 + 7 5.5m + m2 = 0 + 7 Combine like terms: 0 + 7 = 7 5.5m + m2 = 7 The m term is 5.5m. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5m + 7.5625 + m2 = 7 + 7.5625 Reorder the terms: 7.5625 + 5.5m + m2 = 7 + 7.5625 Combine like terms: 7 + 7.5625 = 14.5625 7.5625 + 5.5m + m2 = 14.5625 Factor a perfect square on the left side: (m + 2.75)(m + 2.75) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (m + 2.75) equal to 3.816084381 and -3.816084381.Subproblem 1
m + 2.75 = 3.816084381 Simplifying m + 2.75 = 3.816084381 Reorder the terms: 2.75 + m = 3.816084381 Solving 2.75 + m = 3.816084381 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + m = 3.816084381 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + m = 3.816084381 + -2.75 m = 3.816084381 + -2.75 Combine like terms: 3.816084381 + -2.75 = 1.066084381 m = 1.066084381 Simplifying m = 1.066084381Subproblem 2
m + 2.75 = -3.816084381 Simplifying m + 2.75 = -3.816084381 Reorder the terms: 2.75 + m = -3.816084381 Solving 2.75 + m = -3.816084381 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + m = -3.816084381 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + m = -3.816084381 + -2.75 m = -3.816084381 + -2.75 Combine like terms: -3.816084381 + -2.75 = -6.566084381 m = -6.566084381 Simplifying m = -6.566084381Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.066084381, -6.566084381}
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