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Simplifying 7m(m + -3) = 3m + -14 Reorder the terms: 7m(-3 + m) = 3m + -14 (-3 * 7m + m * 7m) = 3m + -14 (-21m + 7m2) = 3m + -14 Reorder the terms: -21m + 7m2 = -14 + 3m Solving -21m + 7m2 = -14 + 3m Solving for variable 'm'. Reorder the terms: 14 + -21m + -3m + 7m2 = -14 + 3m + 14 + -3m Combine like terms: -21m + -3m = -24m 14 + -24m + 7m2 = -14 + 3m + 14 + -3m Reorder the terms: 14 + -24m + 7m2 = -14 + 14 + 3m + -3m Combine like terms: -14 + 14 = 0 14 + -24m + 7m2 = 0 + 3m + -3m 14 + -24m + 7m2 = 3m + -3m Combine like terms: 3m + -3m = 0 14 + -24m + 7m2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2 + -3.428571429m + m2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.428571429m + -2 + m2 = 0 + -2 Reorder the terms: 2 + -2 + -3.428571429m + m2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.428571429m + m2 = 0 + -2 -3.428571429m + m2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.428571429m + m2 = -2 The m term is -3.428571429m. Take half its coefficient (-1.714285715). Square it (2.938775513) and add it to both sides. Add '2.938775513' to each side of the equation. -3.428571429m + 2.938775513 + m2 = -2 + 2.938775513 Reorder the terms: 2.938775513 + -3.428571429m + m2 = -2 + 2.938775513 Combine like terms: -2 + 2.938775513 = 0.938775513 2.938775513 + -3.428571429m + m2 = 0.938775513 Factor a perfect square on the left side: (m + -1.714285715)(m + -1.714285715) = 0.938775513 Calculate the square root of the right side: 0.968904285 Break this problem into two subproblems by setting (m + -1.714285715) equal to 0.968904285 and -0.968904285.Subproblem 1
m + -1.714285715 = 0.968904285 Simplifying m + -1.714285715 = 0.968904285 Reorder the terms: -1.714285715 + m = 0.968904285 Solving -1.714285715 + m = 0.968904285 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + m = 0.968904285 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + m = 0.968904285 + 1.714285715 m = 0.968904285 + 1.714285715 Combine like terms: 0.968904285 + 1.714285715 = 2.68319 m = 2.68319 Simplifying m = 2.68319Subproblem 2
m + -1.714285715 = -0.968904285 Simplifying m + -1.714285715 = -0.968904285 Reorder the terms: -1.714285715 + m = -0.968904285 Solving -1.714285715 + m = -0.968904285 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + m = -0.968904285 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + m = -0.968904285 + 1.714285715 m = -0.968904285 + 1.714285715 Combine like terms: -0.968904285 + 1.714285715 = 0.74538143 m = 0.74538143 Simplifying m = 0.74538143Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.68319, 0.74538143}
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