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Simplifying -16t2 + 60t + 25 = 0 Reorder the terms: 25 + 60t + -16t2 = 0 Solving 25 + 60t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -1.5625 + -3.75t + t2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + -3.75t + 1.5625 + t2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + -3.75t + t2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + -3.75t + t2 = 0 + 1.5625 -3.75t + t2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 -3.75t + t2 = 1.5625 The t term is -3.75t. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75t + 3.515625 + t2 = 1.5625 + 3.515625 Reorder the terms: 3.515625 + -3.75t + t2 = 1.5625 + 3.515625 Combine like terms: 1.5625 + 3.515625 = 5.078125 3.515625 + -3.75t + t2 = 5.078125 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = 5.078125 Calculate the square root of the right side: 2.253469547 Break this problem into two subproblems by setting (t + -1.875) equal to 2.253469547 and -2.253469547.Subproblem 1
t + -1.875 = 2.253469547 Simplifying t + -1.875 = 2.253469547 Reorder the terms: -1.875 + t = 2.253469547 Solving -1.875 + t = 2.253469547 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = 2.253469547 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 2.253469547 + 1.875 t = 2.253469547 + 1.875 Combine like terms: 2.253469547 + 1.875 = 4.128469547 t = 4.128469547 Simplifying t = 4.128469547Subproblem 2
t + -1.875 = -2.253469547 Simplifying t + -1.875 = -2.253469547 Reorder the terms: -1.875 + t = -2.253469547 Solving -1.875 + t = -2.253469547 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = -2.253469547 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -2.253469547 + 1.875 t = -2.253469547 + 1.875 Combine like terms: -2.253469547 + 1.875 = -0.378469547 t = -0.378469547 Simplifying t = -0.378469547Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.128469547, -0.378469547}
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