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Simplifying (t) = -16t2 + 16t + 4 t = -16t2 + 16t + 4 Reorder the terms: t = 4 + 16t + -16t2 Solving t = 4 + 16t + -16t2 Solving for variable 't'. Reorder the terms: -4 + t + -16t + 16t2 = 4 + 16t + -16t2 + -4 + -16t + 16t2 Combine like terms: t + -16t = -15t -4 + -15t + 16t2 = 4 + 16t + -16t2 + -4 + -16t + 16t2 Reorder the terms: -4 + -15t + 16t2 = 4 + -4 + 16t + -16t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 -4 + -15t + 16t2 = 0 + 16t + -16t + -16t2 + 16t2 -4 + -15t + 16t2 = 16t + -16t + -16t2 + 16t2 Combine like terms: 16t + -16t = 0 -4 + -15t + 16t2 = 0 + -16t2 + 16t2 -4 + -15t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -4 + -15t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.25 + -0.9375t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.9375t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.9375t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.9375t + t2 = 0 + 0.25 -0.9375t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.9375t + t2 = 0.25 The t term is -0.9375t. Take half its coefficient (-0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. -0.9375t + 0.2197265625 + t2 = 0.25 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375t + t2 = 0.25 + 0.2197265625 Combine like terms: 0.25 + 0.2197265625 = 0.4697265625 0.2197265625 + -0.9375t + t2 = 0.4697265625 Factor a perfect square on the left side: (t + -0.46875)(t + -0.46875) = 0.4697265625 Calculate the square root of the right side: 0.685366006 Break this problem into two subproblems by setting (t + -0.46875) equal to 0.685366006 and -0.685366006.Subproblem 1
t + -0.46875 = 0.685366006 Simplifying t + -0.46875 = 0.685366006 Reorder the terms: -0.46875 + t = 0.685366006 Solving -0.46875 + t = 0.685366006 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + t = 0.685366006 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = 0.685366006 + 0.46875 t = 0.685366006 + 0.46875 Combine like terms: 0.685366006 + 0.46875 = 1.154116006 t = 1.154116006 Simplifying t = 1.154116006Subproblem 2
t + -0.46875 = -0.685366006 Simplifying t + -0.46875 = -0.685366006 Reorder the terms: -0.46875 + t = -0.685366006 Solving -0.46875 + t = -0.685366006 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + t = -0.685366006 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = -0.685366006 + 0.46875 t = -0.685366006 + 0.46875 Combine like terms: -0.685366006 + 0.46875 = -0.216616006 t = -0.216616006 Simplifying t = -0.216616006Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.154116006, -0.216616006}
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