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Simplifying -16t2 + 70t + 5 = 0 Reorder the terms: 5 + 70t + -16t2 = 0 Solving 5 + 70t + -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'. -0.3125 + -4.375t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -4.375t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -4.375t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -4.375t + t2 = 0 + 0.3125 -4.375t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -4.375t + t2 = 0.3125 The t term is -4.375t. Take half its coefficient (-2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. -4.375t + 4.78515625 + t2 = 0.3125 + 4.78515625 Reorder the terms: 4.78515625 + -4.375t + t2 = 0.3125 + 4.78515625 Combine like terms: 0.3125 + 4.78515625 = 5.09765625 4.78515625 + -4.375t + t2 = 5.09765625 Factor a perfect square on the left side: (t + -2.1875)(t + -2.1875) = 5.09765625 Calculate the square root of the right side: 2.257798984 Break this problem into two subproblems by setting (t + -2.1875) equal to 2.257798984 and -2.257798984.Subproblem 1
t + -2.1875 = 2.257798984 Simplifying t + -2.1875 = 2.257798984 Reorder the terms: -2.1875 + t = 2.257798984 Solving -2.1875 + t = 2.257798984 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + t = 2.257798984 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + t = 2.257798984 + 2.1875 t = 2.257798984 + 2.1875 Combine like terms: 2.257798984 + 2.1875 = 4.445298984 t = 4.445298984 Simplifying t = 4.445298984Subproblem 2
t + -2.1875 = -2.257798984 Simplifying t + -2.1875 = -2.257798984 Reorder the terms: -2.1875 + t = -2.257798984 Solving -2.1875 + t = -2.257798984 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + t = -2.257798984 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + t = -2.257798984 + 2.1875 t = -2.257798984 + 2.1875 Combine like terms: -2.257798984 + 2.1875 = -0.070298984 t = -0.070298984 Simplifying t = -0.070298984Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.445298984, -0.070298984}
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