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Simplifying -5t2 + 20t + -14.4 = 0 Reorder the terms: -14.4 + 20t + -5t2 = 0 Solving -14.4 + 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'. 2.88 + -4t + t2 = 0 Move the constant term to the right: Add '-2.88' to each side of the equation. 2.88 + -4t + -2.88 + t2 = 0 + -2.88 Reorder the terms: 2.88 + -2.88 + -4t + t2 = 0 + -2.88 Combine like terms: 2.88 + -2.88 = 0.00 0.00 + -4t + t2 = 0 + -2.88 -4t + t2 = 0 + -2.88 Combine like terms: 0 + -2.88 = -2.88 -4t + t2 = -2.88 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 = -2.88 + 4 Reorder the terms: 4 + -4t + t2 = -2.88 + 4 Combine like terms: -2.88 + 4 = 1.12 4 + -4t + t2 = 1.12 Factor a perfect square on the left side: (t + -2)(t + -2) = 1.12 Calculate the square root of the right side: 1.058300524 Break this problem into two subproblems by setting (t + -2) equal to 1.058300524 and -1.058300524.Subproblem 1
t + -2 = 1.058300524 Simplifying t + -2 = 1.058300524 Reorder the terms: -2 + t = 1.058300524 Solving -2 + t = 1.058300524 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 = 1.058300524 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.058300524 + 2 t = 1.058300524 + 2 Combine like terms: 1.058300524 + 2 = 3.058300524 t = 3.058300524 Simplifying t = 3.058300524Subproblem 2
t + -2 = -1.058300524 Simplifying t + -2 = -1.058300524 Reorder the terms: -2 + t = -1.058300524 Solving -2 + t = -1.058300524 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 = -1.058300524 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.058300524 + 2 t = -1.058300524 + 2 Combine like terms: -1.058300524 + 2 = 0.941699476 t = 0.941699476 Simplifying t = 0.941699476Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.058300524, 0.941699476}
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