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Simplifying 30 = -10t2 + 40t + 2 Reorder the terms: 30 = 2 + 40t + -10t2 Solving 30 = 2 + 40t + -10t2 Solving for variable 't'. Combine like terms: 30 + -2 = 28 28 + -40t + 10t2 = 2 + 40t + -10t2 + -2 + -40t + 10t2 Reorder the terms: 28 + -40t + 10t2 = 2 + -2 + 40t + -40t + -10t2 + 10t2 Combine like terms: 2 + -2 = 0 28 + -40t + 10t2 = 0 + 40t + -40t + -10t2 + 10t2 28 + -40t + 10t2 = 40t + -40t + -10t2 + 10t2 Combine like terms: 40t + -40t = 0 28 + -40t + 10t2 = 0 + -10t2 + 10t2 28 + -40t + 10t2 = -10t2 + 10t2 Combine like terms: -10t2 + 10t2 = 0 28 + -40t + 10t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(14 + -20t + 5t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + -20t + 5t2)' equal to zero and attempt to solve: Simplifying 14 + -20t + 5t2 = 0 Solving 14 + -20t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.8 + -4t + t2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + -4t + -2.8 + t2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + -4t + t2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + -4t + t2 = 0 + -2.8 -4t + t2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 -4t + t2 = -2.8 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = -2.8 + 4 Reorder the terms: 4 + -4t + t2 = -2.8 + 4 Combine like terms: -2.8 + 4 = 1.2 4 + -4t + t2 = 1.2 Factor a perfect square on the left side: (t + -2)(t + -2) = 1.2 Calculate the square root of the right side: 1.095445115 Break this problem into two subproblems by setting (t + -2) equal to 1.095445115 and -1.095445115.Subproblem 1
t + -2 = 1.095445115 Simplifying t + -2 = 1.095445115 Reorder the terms: -2 + t = 1.095445115 Solving -2 + t = 1.095445115 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1.095445115 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.095445115 + 2 t = 1.095445115 + 2 Combine like terms: 1.095445115 + 2 = 3.095445115 t = 3.095445115 Simplifying t = 3.095445115Subproblem 2
t + -2 = -1.095445115 Simplifying t + -2 = -1.095445115 Reorder the terms: -2 + t = -1.095445115 Solving -2 + t = -1.095445115 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1.095445115 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.095445115 + 2 t = -1.095445115 + 2 Combine like terms: -1.095445115 + 2 = 0.904554885 t = 0.904554885 Simplifying t = 0.904554885Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.095445115, 0.904554885}Solution
t = {3.095445115, 0.904554885}
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