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Simplifying 7m2 = 10m + 22 Reorder the terms: 7m2 = 22 + 10m Solving 7m2 = 22 + 10m Solving for variable 'm'. Reorder the terms: -22 + -10m + 7m2 = 22 + 10m + -22 + -10m Reorder the terms: -22 + -10m + 7m2 = 22 + -22 + 10m + -10m Combine like terms: 22 + -22 = 0 -22 + -10m + 7m2 = 0 + 10m + -10m -22 + -10m + 7m2 = 10m + -10m Combine like terms: 10m + -10m = 0 -22 + -10m + 7m2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.142857143 + -1.428571429m + m2 = 0 Move the constant term to the right: Add '3.142857143' to each side of the equation. -3.142857143 + -1.428571429m + 3.142857143 + m2 = 0 + 3.142857143 Reorder the terms: -3.142857143 + 3.142857143 + -1.428571429m + m2 = 0 + 3.142857143 Combine like terms: -3.142857143 + 3.142857143 = 0.000000000 0.000000000 + -1.428571429m + m2 = 0 + 3.142857143 -1.428571429m + m2 = 0 + 3.142857143 Combine like terms: 0 + 3.142857143 = 3.142857143 -1.428571429m + m2 = 3.142857143 The m term is -1.428571429m. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429m + 0.5102040819 + m2 = 3.142857143 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429m + m2 = 3.142857143 + 0.5102040819 Combine like terms: 3.142857143 + 0.5102040819 = 3.6530612249 0.5102040819 + -1.428571429m + m2 = 3.6530612249 Factor a perfect square on the left side: (m + -0.7142857145)(m + -0.7142857145) = 3.6530612249 Calculate the square root of the right side: 1.911298309 Break this problem into two subproblems by setting (m + -0.7142857145) equal to 1.911298309 and -1.911298309.Subproblem 1
m + -0.7142857145 = 1.911298309 Simplifying m + -0.7142857145 = 1.911298309 Reorder the terms: -0.7142857145 + m = 1.911298309 Solving -0.7142857145 + m = 1.911298309 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + m = 1.911298309 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + m = 1.911298309 + 0.7142857145 m = 1.911298309 + 0.7142857145 Combine like terms: 1.911298309 + 0.7142857145 = 2.6255840235 m = 2.6255840235 Simplifying m = 2.6255840235Subproblem 2
m + -0.7142857145 = -1.911298309 Simplifying m + -0.7142857145 = -1.911298309 Reorder the terms: -0.7142857145 + m = -1.911298309 Solving -0.7142857145 + m = -1.911298309 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + m = -1.911298309 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + m = -1.911298309 + 0.7142857145 m = -1.911298309 + 0.7142857145 Combine like terms: -1.911298309 + 0.7142857145 = -1.1970125945 m = -1.1970125945 Simplifying m = -1.1970125945Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.6255840235, -1.1970125945}
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