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Simplifying -7m(3m + 7) + 3(m + 1) = 0 Reorder the terms: -7m(7 + 3m) + 3(m + 1) = 0 (7 * -7m + 3m * -7m) + 3(m + 1) = 0 (-49m + -21m2) + 3(m + 1) = 0 Reorder the terms: -49m + -21m2 + 3(1 + m) = 0 -49m + -21m2 + (1 * 3 + m * 3) = 0 -49m + -21m2 + (3 + 3m) = 0 Reorder the terms: 3 + -49m + 3m + -21m2 = 0 Combine like terms: -49m + 3m = -46m 3 + -46m + -21m2 = 0 Solving 3 + -46m + -21m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -21 the coefficient of the squared term: Divide each side by '-21'. -0.1428571429 + 2.19047619m + m2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 2.19047619m + 0.1428571429 + m2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 2.19047619m + m2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 2.19047619m + m2 = 0 + 0.1428571429 2.19047619m + m2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 2.19047619m + m2 = 0.1428571429 The m term is 2.19047619m. Take half its coefficient (1.095238095). Square it (1.199546485) and add it to both sides. Add '1.199546485' to each side of the equation. 2.19047619m + 1.199546485 + m2 = 0.1428571429 + 1.199546485 Reorder the terms: 1.199546485 + 2.19047619m + m2 = 0.1428571429 + 1.199546485 Combine like terms: 0.1428571429 + 1.199546485 = 1.3424036279 1.199546485 + 2.19047619m + m2 = 1.3424036279 Factor a perfect square on the left side: (m + 1.095238095)(m + 1.095238095) = 1.3424036279 Calculate the square root of the right side: 1.158621434 Break this problem into two subproblems by setting (m + 1.095238095) equal to 1.158621434 and -1.158621434.Subproblem 1
m + 1.095238095 = 1.158621434 Simplifying m + 1.095238095 = 1.158621434 Reorder the terms: 1.095238095 + m = 1.158621434 Solving 1.095238095 + m = 1.158621434 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.095238095' to each side of the equation. 1.095238095 + -1.095238095 + m = 1.158621434 + -1.095238095 Combine like terms: 1.095238095 + -1.095238095 = 0.000000000 0.000000000 + m = 1.158621434 + -1.095238095 m = 1.158621434 + -1.095238095 Combine like terms: 1.158621434 + -1.095238095 = 0.063383339 m = 0.063383339 Simplifying m = 0.063383339Subproblem 2
m + 1.095238095 = -1.158621434 Simplifying m + 1.095238095 = -1.158621434 Reorder the terms: 1.095238095 + m = -1.158621434 Solving 1.095238095 + m = -1.158621434 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.095238095' to each side of the equation. 1.095238095 + -1.095238095 + m = -1.158621434 + -1.095238095 Combine like terms: 1.095238095 + -1.095238095 = 0.000000000 0.000000000 + m = -1.158621434 + -1.095238095 m = -1.158621434 + -1.095238095 Combine like terms: -1.158621434 + -1.095238095 = -2.253859529 m = -2.253859529 Simplifying m = -2.253859529Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.063383339, -2.253859529}
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