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Simplifying 0 = 8 + -26m + -21m2 Solving 0 = 8 + -26m + -21m2 Solving for variable 'm'. Combine like terms: 0 + -8 = -8 -8 + 26m + 21m2 = 8 + -26m + -21m2 + -8 + 26m + 21m2 Reorder the terms: -8 + 26m + 21m2 = 8 + -8 + -26m + 26m + -21m2 + 21m2 Combine like terms: 8 + -8 = 0 -8 + 26m + 21m2 = 0 + -26m + 26m + -21m2 + 21m2 -8 + 26m + 21m2 = -26m + 26m + -21m2 + 21m2 Combine like terms: -26m + 26m = 0 -8 + 26m + 21m2 = 0 + -21m2 + 21m2 -8 + 26m + 21m2 = -21m2 + 21m2 Combine like terms: -21m2 + 21m2 = 0 -8 + 26m + 21m2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.380952381 + 1.238095238m + m2 = 0 Move the constant term to the right: Add '0.380952381' to each side of the equation. -0.380952381 + 1.238095238m + 0.380952381 + m2 = 0 + 0.380952381 Reorder the terms: -0.380952381 + 0.380952381 + 1.238095238m + m2 = 0 + 0.380952381 Combine like terms: -0.380952381 + 0.380952381 = 0.000000000 0.000000000 + 1.238095238m + m2 = 0 + 0.380952381 1.238095238m + m2 = 0 + 0.380952381 Combine like terms: 0 + 0.380952381 = 0.380952381 1.238095238m + m2 = 0.380952381 The m term is 1.238095238m. Take half its coefficient (0.619047619). Square it (0.3832199546) and add it to both sides. Add '0.3832199546' to each side of the equation. 1.238095238m + 0.3832199546 + m2 = 0.380952381 + 0.3832199546 Reorder the terms: 0.3832199546 + 1.238095238m + m2 = 0.380952381 + 0.3832199546 Combine like terms: 0.380952381 + 0.3832199546 = 0.7641723356 0.3832199546 + 1.238095238m + m2 = 0.7641723356 Factor a perfect square on the left side: (m + 0.619047619)(m + 0.619047619) = 0.7641723356 Calculate the square root of the right side: 0.874169512 Break this problem into two subproblems by setting (m + 0.619047619) equal to 0.874169512 and -0.874169512.Subproblem 1
m + 0.619047619 = 0.874169512 Simplifying m + 0.619047619 = 0.874169512 Reorder the terms: 0.619047619 + m = 0.874169512 Solving 0.619047619 + m = 0.874169512 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.619047619' to each side of the equation. 0.619047619 + -0.619047619 + m = 0.874169512 + -0.619047619 Combine like terms: 0.619047619 + -0.619047619 = 0.000000000 0.000000000 + m = 0.874169512 + -0.619047619 m = 0.874169512 + -0.619047619 Combine like terms: 0.874169512 + -0.619047619 = 0.255121893 m = 0.255121893 Simplifying m = 0.255121893Subproblem 2
m + 0.619047619 = -0.874169512 Simplifying m + 0.619047619 = -0.874169512 Reorder the terms: 0.619047619 + m = -0.874169512 Solving 0.619047619 + m = -0.874169512 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.619047619' to each side of the equation. 0.619047619 + -0.619047619 + m = -0.874169512 + -0.619047619 Combine like terms: 0.619047619 + -0.619047619 = 0.000000000 0.000000000 + m = -0.874169512 + -0.619047619 m = -0.874169512 + -0.619047619 Combine like terms: -0.874169512 + -0.619047619 = -1.493217131 m = -1.493217131 Simplifying m = -1.493217131Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.255121893, -1.493217131}
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