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Simplifying 29.50 = 19.50 + 0.25m(m + -200) Reorder the terms: 29.50 = 19.50 + 0.25m(-200 + m) 29.50 = 19.50 + (-200 * 0.25m + m * 0.25m) 29.50 = 19.50 + (-50m + 0.25m2) Solving 29.50 = 19.50 + -50m + 0.25m2 Solving for variable 'm'. Combine like terms: 29.50 + -19.50 = 10 10 + 50m + -0.25m2 = 19.50 + -50m + 0.25m2 + -19.50 + 50m + -0.25m2 Reorder the terms: 10 + 50m + -0.25m2 = 19.50 + -19.50 + -50m + 50m + 0.25m2 + -0.25m2 Combine like terms: 19.50 + -19.50 = 0.00 10 + 50m + -0.25m2 = 0.00 + -50m + 50m + 0.25m2 + -0.25m2 10 + 50m + -0.25m2 = -50m + 50m + 0.25m2 + -0.25m2 Combine like terms: -50m + 50m = 0 10 + 50m + -0.25m2 = 0 + 0.25m2 + -0.25m2 10 + 50m + -0.25m2 = 0.25m2 + -0.25m2 Combine like terms: 0.25m2 + -0.25m2 = 0.00 10 + 50m + -0.25m2 = 0.00 Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. -40 + -200m + m2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -200m + 40 + m2 = 0 + 40 Reorder the terms: -40 + 40 + -200m + m2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -200m + m2 = 0 + 40 -200m + m2 = 0 + 40 Combine like terms: 0 + 40 = 40 -200m + m2 = 40 The m term is -200m. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200m + 10000 + m2 = 40 + 10000 Reorder the terms: 10000 + -200m + m2 = 40 + 10000 Combine like terms: 40 + 10000 = 10040 10000 + -200m + m2 = 10040 Factor a perfect square on the left side: (m + -100)(m + -100) = 10040 Calculate the square root of the right side: 100.199800399 Break this problem into two subproblems by setting (m + -100) equal to 100.199800399 and -100.199800399.Subproblem 1
m + -100 = 100.199800399 Simplifying m + -100 = 100.199800399 Reorder the terms: -100 + m = 100.199800399 Solving -100 + m = 100.199800399 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + m = 100.199800399 + 100 Combine like terms: -100 + 100 = 0 0 + m = 100.199800399 + 100 m = 100.199800399 + 100 Combine like terms: 100.199800399 + 100 = 200.199800399 m = 200.199800399 Simplifying m = 200.199800399Subproblem 2
m + -100 = -100.199800399 Simplifying m + -100 = -100.199800399 Reorder the terms: -100 + m = -100.199800399 Solving -100 + m = -100.199800399 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + m = -100.199800399 + 100 Combine like terms: -100 + 100 = 0 0 + m = -100.199800399 + 100 m = -100.199800399 + 100 Combine like terms: -100.199800399 + 100 = -0.199800399 m = -0.199800399 Simplifying m = -0.199800399Solution
The solution to the problem is based on the solutions from the subproblems. m = {200.199800399, -0.199800399}
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