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Simplifying 7 + 6.2m = 4.3m(0.5m + 2.4) Reorder the terms: 7 + 6.2m = 4.3m(2.4 + 0.5m) 7 + 6.2m = (2.4 * 4.3m + 0.5m * 4.3m) 7 + 6.2m = (10.32m + 2.15m2) Solving 7 + 6.2m = 10.32m + 2.15m2 Solving for variable 'm'. Combine like terms: 6.2m + -10.32m = -4.12m 7 + -4.12m + -2.15m2 = 10.32m + 2.15m2 + -10.32m + -2.15m2 Reorder the terms: 7 + -4.12m + -2.15m2 = 10.32m + -10.32m + 2.15m2 + -2.15m2 Combine like terms: 10.32m + -10.32m = 0.00 7 + -4.12m + -2.15m2 = 0.00 + 2.15m2 + -2.15m2 7 + -4.12m + -2.15m2 = 2.15m2 + -2.15m2 Combine like terms: 2.15m2 + -2.15m2 = 0.00 7 + -4.12m + -2.15m2 = 0.00 Begin completing the square. Divide all terms by -2.15 the coefficient of the squared term: Divide each side by '-2.15'. -3.255813953 + 1.91627907m + m2 = 0 Move the constant term to the right: Add '3.255813953' to each side of the equation. -3.255813953 + 1.91627907m + 3.255813953 + m2 = 0 + 3.255813953 Reorder the terms: -3.255813953 + 3.255813953 + 1.91627907m + m2 = 0 + 3.255813953 Combine like terms: -3.255813953 + 3.255813953 = 0.000000000 0.000000000 + 1.91627907m + m2 = 0 + 3.255813953 1.91627907m + m2 = 0 + 3.255813953 Combine like terms: 0 + 3.255813953 = 3.255813953 1.91627907m + m2 = 3.255813953 The m term is 1.91627907m. Take half its coefficient (0.958139535). Square it (0.9180313685) and add it to both sides. Add '0.9180313685' to each side of the equation. 1.91627907m + 0.9180313685 + m2 = 3.255813953 + 0.9180313685 Reorder the terms: 0.9180313685 + 1.91627907m + m2 = 3.255813953 + 0.9180313685 Combine like terms: 3.255813953 + 0.9180313685 = 4.1738453215 0.9180313685 + 1.91627907m + m2 = 4.1738453215 Factor a perfect square on the left side: (m + 0.958139535)(m + 0.958139535) = 4.1738453215 Calculate the square root of the right side: 2.0429991 Break this problem into two subproblems by setting (m + 0.958139535) equal to 2.0429991 and -2.0429991.Subproblem 1
m + 0.958139535 = 2.0429991 Simplifying m + 0.958139535 = 2.0429991 Reorder the terms: 0.958139535 + m = 2.0429991 Solving 0.958139535 + m = 2.0429991 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.958139535' to each side of the equation. 0.958139535 + -0.958139535 + m = 2.0429991 + -0.958139535 Combine like terms: 0.958139535 + -0.958139535 = 0.000000000 0.000000000 + m = 2.0429991 + -0.958139535 m = 2.0429991 + -0.958139535 Combine like terms: 2.0429991 + -0.958139535 = 1.084859565 m = 1.084859565 Simplifying m = 1.084859565Subproblem 2
m + 0.958139535 = -2.0429991 Simplifying m + 0.958139535 = -2.0429991 Reorder the terms: 0.958139535 + m = -2.0429991 Solving 0.958139535 + m = -2.0429991 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.958139535' to each side of the equation. 0.958139535 + -0.958139535 + m = -2.0429991 + -0.958139535 Combine like terms: 0.958139535 + -0.958139535 = 0.000000000 0.000000000 + m = -2.0429991 + -0.958139535 m = -2.0429991 + -0.958139535 Combine like terms: -2.0429991 + -0.958139535 = -3.001138635 m = -3.001138635 Simplifying m = -3.001138635Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.084859565, -3.001138635}
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