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Simplifying -5t2 + -20t + 96 = 0 Reorder the terms: 96 + -20t + -5t2 = 0 Solving 96 + -20t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -19.2 + 4t + t2 = 0 Move the constant term to the right: Add '19.2' to each side of the equation. -19.2 + 4t + 19.2 + t2 = 0 + 19.2 Reorder the terms: -19.2 + 19.2 + 4t + t2 = 0 + 19.2 Combine like terms: -19.2 + 19.2 = 0.0 0.0 + 4t + t2 = 0 + 19.2 4t + t2 = 0 + 19.2 Combine like terms: 0 + 19.2 = 19.2 4t + t2 = 19.2 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 = 19.2 + 4 Reorder the terms: 4 + 4t + t2 = 19.2 + 4 Combine like terms: 19.2 + 4 = 23.2 4 + 4t + t2 = 23.2 Factor a perfect square on the left side: (t + 2)(t + 2) = 23.2 Calculate the square root of the right side: 4.816637832 Break this problem into two subproblems by setting (t + 2) equal to 4.816637832 and -4.816637832.Subproblem 1
t + 2 = 4.816637832 Simplifying t + 2 = 4.816637832 Reorder the terms: 2 + t = 4.816637832 Solving 2 + t = 4.816637832 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 = 4.816637832 + -2 Combine like terms: 2 + -2 = 0 0 + t = 4.816637832 + -2 t = 4.816637832 + -2 Combine like terms: 4.816637832 + -2 = 2.816637832 t = 2.816637832 Simplifying t = 2.816637832Subproblem 2
t + 2 = -4.816637832 Simplifying t + 2 = -4.816637832 Reorder the terms: 2 + t = -4.816637832 Solving 2 + t = -4.816637832 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 = -4.816637832 + -2 Combine like terms: 2 + -2 = 0 0 + t = -4.816637832 + -2 t = -4.816637832 + -2 Combine like terms: -4.816637832 + -2 = -6.816637832 t = -6.816637832 Simplifying t = -6.816637832Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.816637832, -6.816637832}
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