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Simplifying -4t2 + 20t + 25 = 0 Reorder the terms: 25 + 20t + -4t2 = 0 Solving 25 + 20t + -4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -6.25 + -5t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -5t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -5t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -5t + t2 = 0 + 6.25 -5t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -5t + t2 = 6.25 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 6.25 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 6.25 + 6.25 Combine like terms: 6.25 + 6.25 = 12.5 6.25 + -5t + t2 = 12.5 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (t + -2.5) equal to 3.535533906 and -3.535533906.Subproblem 1
t + -2.5 = 3.535533906 Simplifying t + -2.5 = 3.535533906 Reorder the terms: -2.5 + t = 3.535533906 Solving -2.5 + t = 3.535533906 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 3.535533906 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 3.535533906 + 2.5 t = 3.535533906 + 2.5 Combine like terms: 3.535533906 + 2.5 = 6.035533906 t = 6.035533906 Simplifying t = 6.035533906Subproblem 2
t + -2.5 = -3.535533906 Simplifying t + -2.5 = -3.535533906 Reorder the terms: -2.5 + t = -3.535533906 Solving -2.5 + t = -3.535533906 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -3.535533906 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -3.535533906 + 2.5 t = -3.535533906 + 2.5 Combine like terms: -3.535533906 + 2.5 = -1.035533906 t = -1.035533906 Simplifying t = -1.035533906Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.035533906, -1.035533906}
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