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Simplifying -4t2 + 16t + 5 = 0 Reorder the terms: 5 + 16t + -4t2 = 0 Solving 5 + 16t + -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'. -1.25 + -4t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -4t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -4t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -4t + t2 = 0 + 1.25 -4t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -4t + t2 = 1.25 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 = 1.25 + 4 Reorder the terms: 4 + -4t + t2 = 1.25 + 4 Combine like terms: 1.25 + 4 = 5.25 4 + -4t + t2 = 5.25 Factor a perfect square on the left side: (t + -2)(t + -2) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (t + -2) equal to 2.291287847 and -2.291287847.Subproblem 1
t + -2 = 2.291287847 Simplifying t + -2 = 2.291287847 Reorder the terms: -2 + t = 2.291287847 Solving -2 + t = 2.291287847 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 = 2.291287847 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.291287847 + 2 t = 2.291287847 + 2 Combine like terms: 2.291287847 + 2 = 4.291287847 t = 4.291287847 Simplifying t = 4.291287847Subproblem 2
t + -2 = -2.291287847 Simplifying t + -2 = -2.291287847 Reorder the terms: -2 + t = -2.291287847 Solving -2 + t = -2.291287847 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 = -2.291287847 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.291287847 + 2 t = -2.291287847 + 2 Combine like terms: -2.291287847 + 2 = -0.291287847 t = -0.291287847 Simplifying t = -0.291287847Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.291287847, -0.291287847}
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