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Simplifying 7m(3m + -1) = 4m + 5 Reorder the terms: 7m(-1 + 3m) = 4m + 5 (-1 * 7m + 3m * 7m) = 4m + 5 (-7m + 21m2) = 4m + 5 Reorder the terms: -7m + 21m2 = 5 + 4m Solving -7m + 21m2 = 5 + 4m Solving for variable 'm'. Reorder the terms: -5 + -7m + -4m + 21m2 = 5 + 4m + -5 + -4m Combine like terms: -7m + -4m = -11m -5 + -11m + 21m2 = 5 + 4m + -5 + -4m Reorder the terms: -5 + -11m + 21m2 = 5 + -5 + 4m + -4m Combine like terms: 5 + -5 = 0 -5 + -11m + 21m2 = 0 + 4m + -4m -5 + -11m + 21m2 = 4m + -4m Combine like terms: 4m + -4m = 0 -5 + -11m + 21m2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.2380952381 + -0.5238095238m + m2 = 0 Move the constant term to the right: Add '0.2380952381' to each side of the equation. -0.2380952381 + -0.5238095238m + 0.2380952381 + m2 = 0 + 0.2380952381 Reorder the terms: -0.2380952381 + 0.2380952381 + -0.5238095238m + m2 = 0 + 0.2380952381 Combine like terms: -0.2380952381 + 0.2380952381 = 0.0000000000 0.0000000000 + -0.5238095238m + m2 = 0 + 0.2380952381 -0.5238095238m + m2 = 0 + 0.2380952381 Combine like terms: 0 + 0.2380952381 = 0.2380952381 -0.5238095238m + m2 = 0.2380952381 The m term is -0.5238095238m. Take half its coefficient (-0.2619047619). Square it (0.06859410431) and add it to both sides. Add '0.06859410431' to each side of the equation. -0.5238095238m + 0.06859410431 + m2 = 0.2380952381 + 0.06859410431 Reorder the terms: 0.06859410431 + -0.5238095238m + m2 = 0.2380952381 + 0.06859410431 Combine like terms: 0.2380952381 + 0.06859410431 = 0.30668934241 0.06859410431 + -0.5238095238m + m2 = 0.30668934241 Factor a perfect square on the left side: (m + -0.2619047619)(m + -0.2619047619) = 0.30668934241 Calculate the square root of the right side: 0.553795398 Break this problem into two subproblems by setting (m + -0.2619047619) equal to 0.553795398 and -0.553795398.Subproblem 1
m + -0.2619047619 = 0.553795398 Simplifying m + -0.2619047619 = 0.553795398 Reorder the terms: -0.2619047619 + m = 0.553795398 Solving -0.2619047619 + m = 0.553795398 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2619047619' to each side of the equation. -0.2619047619 + 0.2619047619 + m = 0.553795398 + 0.2619047619 Combine like terms: -0.2619047619 + 0.2619047619 = 0.0000000000 0.0000000000 + m = 0.553795398 + 0.2619047619 m = 0.553795398 + 0.2619047619 Combine like terms: 0.553795398 + 0.2619047619 = 0.8157001599 m = 0.8157001599 Simplifying m = 0.8157001599Subproblem 2
m + -0.2619047619 = -0.553795398 Simplifying m + -0.2619047619 = -0.553795398 Reorder the terms: -0.2619047619 + m = -0.553795398 Solving -0.2619047619 + m = -0.553795398 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2619047619' to each side of the equation. -0.2619047619 + 0.2619047619 + m = -0.553795398 + 0.2619047619 Combine like terms: -0.2619047619 + 0.2619047619 = 0.0000000000 0.0000000000 + m = -0.553795398 + 0.2619047619 m = -0.553795398 + 0.2619047619 Combine like terms: -0.553795398 + 0.2619047619 = -0.2918906361 m = -0.2918906361 Simplifying m = -0.2918906361Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.8157001599, -0.2918906361}
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