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Simplifying 11m2 + 2m = 8 Reorder the terms: 2m + 11m2 = 8 Solving 2m + 11m2 = 8 Solving for variable 'm'. Reorder the terms: -8 + 2m + 11m2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 2m + 11m2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.7272727273 + 0.1818181818m + m2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + 0.1818181818m + 0.7272727273 + m2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + 0.1818181818m + m2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + 0.1818181818m + m2 = 0 + 0.7272727273 0.1818181818m + m2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 0.1818181818m + m2 = 0.7272727273 The m term is 0.1818181818m. Take half its coefficient (0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. 0.1818181818m + 0.008264462808 + m2 = 0.7272727273 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818m + m2 = 0.7272727273 + 0.008264462808 Combine like terms: 0.7272727273 + 0.008264462808 = 0.735537190108 0.008264462808 + 0.1818181818m + m2 = 0.735537190108 Factor a perfect square on the left side: (m + 0.0909090909)(m + 0.0909090909) = 0.735537190108 Calculate the square root of the right side: 0.857634648 Break this problem into two subproblems by setting (m + 0.0909090909) equal to 0.857634648 and -0.857634648.Subproblem 1
m + 0.0909090909 = 0.857634648 Simplifying m + 0.0909090909 = 0.857634648 Reorder the terms: 0.0909090909 + m = 0.857634648 Solving 0.0909090909 + m = 0.857634648 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + m = 0.857634648 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + m = 0.857634648 + -0.0909090909 m = 0.857634648 + -0.0909090909 Combine like terms: 0.857634648 + -0.0909090909 = 0.7667255571 m = 0.7667255571 Simplifying m = 0.7667255571Subproblem 2
m + 0.0909090909 = -0.857634648 Simplifying m + 0.0909090909 = -0.857634648 Reorder the terms: 0.0909090909 + m = -0.857634648 Solving 0.0909090909 + m = -0.857634648 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + m = -0.857634648 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + m = -0.857634648 + -0.0909090909 m = -0.857634648 + -0.0909090909 Combine like terms: -0.857634648 + -0.0909090909 = -0.9485437389 m = -0.9485437389 Simplifying m = -0.9485437389Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.7667255571, -0.9485437389}
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