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Simplifying -16t2 + 100t + 5 = 0 Reorder the terms: 5 + 100t + -16t2 = 0 Solving 5 + 100t + -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 + -6.25t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -6.25t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -6.25t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -6.25t + t2 = 0 + 0.3125 -6.25t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -6.25t + t2 = 0.3125 The t term is -6.25t. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25t + 9.765625 + t2 = 0.3125 + 9.765625 Reorder the terms: 9.765625 + -6.25t + t2 = 0.3125 + 9.765625 Combine like terms: 0.3125 + 9.765625 = 10.078125 9.765625 + -6.25t + t2 = 10.078125 Factor a perfect square on the left side: (t + -3.125)(t + -3.125) = 10.078125 Calculate the square root of the right side: 3.174606275 Break this problem into two subproblems by setting (t + -3.125) equal to 3.174606275 and -3.174606275.Subproblem 1
t + -3.125 = 3.174606275 Simplifying t + -3.125 = 3.174606275 Reorder the terms: -3.125 + t = 3.174606275 Solving -3.125 + t = 3.174606275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = 3.174606275 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = 3.174606275 + 3.125 t = 3.174606275 + 3.125 Combine like terms: 3.174606275 + 3.125 = 6.299606275 t = 6.299606275 Simplifying t = 6.299606275Subproblem 2
t + -3.125 = -3.174606275 Simplifying t + -3.125 = -3.174606275 Reorder the terms: -3.125 + t = -3.174606275 Solving -3.125 + t = -3.174606275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = -3.174606275 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = -3.174606275 + 3.125 t = -3.174606275 + 3.125 Combine like terms: -3.174606275 + 3.125 = -0.049606275 t = -0.049606275 Simplifying t = -0.049606275Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.299606275, -0.049606275}
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