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Simplifying 10 = 0.25t2 + -6t + 5 Reorder the terms: 10 = 5 + -6t + 0.25t2 Solving 10 = 5 + -6t + 0.25t2 Solving for variable 't'. Combine like terms: 10 + -5 = 5 5 + 6t + -0.25t2 = 5 + -6t + 0.25t2 + -5 + 6t + -0.25t2 Reorder the terms: 5 + 6t + -0.25t2 = 5 + -5 + -6t + 6t + 0.25t2 + -0.25t2 Combine like terms: 5 + -5 = 0 5 + 6t + -0.25t2 = 0 + -6t + 6t + 0.25t2 + -0.25t2 5 + 6t + -0.25t2 = -6t + 6t + 0.25t2 + -0.25t2 Combine like terms: -6t + 6t = 0 5 + 6t + -0.25t2 = 0 + 0.25t2 + -0.25t2 5 + 6t + -0.25t2 = 0.25t2 + -0.25t2 Combine like terms: 0.25t2 + -0.25t2 = 0.00 5 + 6t + -0.25t2 = 0.00 Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. -20 + -24t + t2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -24t + 20 + t2 = 0 + 20 Reorder the terms: -20 + 20 + -24t + t2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -24t + t2 = 0 + 20 -24t + t2 = 0 + 20 Combine like terms: 0 + 20 = 20 -24t + t2 = 20 The t term is -24t. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24t + 144 + t2 = 20 + 144 Reorder the terms: 144 + -24t + t2 = 20 + 144 Combine like terms: 20 + 144 = 164 144 + -24t + t2 = 164 Factor a perfect square on the left side: (t + -12)(t + -12) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (t + -12) equal to 12.806248475 and -12.806248475.Subproblem 1
t + -12 = 12.806248475 Simplifying t + -12 = 12.806248475 Reorder the terms: -12 + t = 12.806248475 Solving -12 + t = 12.806248475 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = 12.806248475 + 12 Combine like terms: -12 + 12 = 0 0 + t = 12.806248475 + 12 t = 12.806248475 + 12 Combine like terms: 12.806248475 + 12 = 24.806248475 t = 24.806248475 Simplifying t = 24.806248475Subproblem 2
t + -12 = -12.806248475 Simplifying t + -12 = -12.806248475 Reorder the terms: -12 + t = -12.806248475 Solving -12 + t = -12.806248475 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = -12.806248475 + 12 Combine like terms: -12 + 12 = 0 0 + t = -12.806248475 + 12 t = -12.806248475 + 12 Combine like terms: -12.806248475 + 12 = -0.806248475 t = -0.806248475 Simplifying t = -0.806248475Solution
The solution to the problem is based on the solutions from the subproblems. t = {24.806248475, -0.806248475}
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