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Simplifying 185 = 2.5t2 + -50t + -187.5 Reorder the terms: 185 = -187.5 + -50t + 2.5t2 Solving 185 = -187.5 + -50t + 2.5t2 Solving for variable 't'. Combine like terms: 185 + 187.5 = 372.5 372.5 + 50t + -2.5t2 = -187.5 + -50t + 2.5t2 + 187.5 + 50t + -2.5t2 Reorder the terms: 372.5 + 50t + -2.5t2 = -187.5 + 187.5 + -50t + 50t + 2.5t2 + -2.5t2 Combine like terms: -187.5 + 187.5 = 0.0 372.5 + 50t + -2.5t2 = 0.0 + -50t + 50t + 2.5t2 + -2.5t2 372.5 + 50t + -2.5t2 = -50t + 50t + 2.5t2 + -2.5t2 Combine like terms: -50t + 50t = 0 372.5 + 50t + -2.5t2 = 0 + 2.5t2 + -2.5t2 372.5 + 50t + -2.5t2 = 2.5t2 + -2.5t2 Combine like terms: 2.5t2 + -2.5t2 = 0.0 372.5 + 50t + -2.5t2 = 0.0 Begin completing the square. Divide all terms by -2.5 the coefficient of the squared term: Divide each side by '-2.5'. -149 + -20t + t2 = 0 Move the constant term to the right: Add '149' to each side of the equation. -149 + -20t + 149 + t2 = 0 + 149 Reorder the terms: -149 + 149 + -20t + t2 = 0 + 149 Combine like terms: -149 + 149 = 0 0 + -20t + t2 = 0 + 149 -20t + t2 = 0 + 149 Combine like terms: 0 + 149 = 149 -20t + t2 = 149 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = 149 + 100 Reorder the terms: 100 + -20t + t2 = 149 + 100 Combine like terms: 149 + 100 = 249 100 + -20t + t2 = 249 Factor a perfect square on the left side: (t + -10)(t + -10) = 249 Calculate the square root of the right side: 15.779733838 Break this problem into two subproblems by setting (t + -10) equal to 15.779733838 and -15.779733838.Subproblem 1
t + -10 = 15.779733838 Simplifying t + -10 = 15.779733838 Reorder the terms: -10 + t = 15.779733838 Solving -10 + t = 15.779733838 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 15.779733838 + 10 Combine like terms: -10 + 10 = 0 0 + t = 15.779733838 + 10 t = 15.779733838 + 10 Combine like terms: 15.779733838 + 10 = 25.779733838 t = 25.779733838 Simplifying t = 25.779733838Subproblem 2
t + -10 = -15.779733838 Simplifying t + -10 = -15.779733838 Reorder the terms: -10 + t = -15.779733838 Solving -10 + t = -15.779733838 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -15.779733838 + 10 Combine like terms: -10 + 10 = 0 0 + t = -15.779733838 + 10 t = -15.779733838 + 10 Combine like terms: -15.779733838 + 10 = -5.779733838 t = -5.779733838 Simplifying t = -5.779733838Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.779733838, -5.779733838}
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