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Simplifying -16t2 + 8t + 87 = 0 Reorder the terms: 87 + 8t + -16t2 = 0 Solving 87 + 8t + -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'. -5.4375 + -0.5t + t2 = 0 Move the constant term to the right: Add '5.4375' to each side of the equation. -5.4375 + -0.5t + 5.4375 + t2 = 0 + 5.4375 Reorder the terms: -5.4375 + 5.4375 + -0.5t + t2 = 0 + 5.4375 Combine like terms: -5.4375 + 5.4375 = 0.0000 0.0000 + -0.5t + t2 = 0 + 5.4375 -0.5t + t2 = 0 + 5.4375 Combine like terms: 0 + 5.4375 = 5.4375 -0.5t + t2 = 5.4375 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = 5.4375 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 5.4375 + 0.0625 Combine like terms: 5.4375 + 0.0625 = 5.5 0.0625 + -0.5t + t2 = 5.5 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (t + -0.25) equal to 2.34520788 and -2.34520788.Subproblem 1
t + -0.25 = 2.34520788 Simplifying t + -0.25 = 2.34520788 Reorder the terms: -0.25 + t = 2.34520788 Solving -0.25 + t = 2.34520788 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = 2.34520788 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 2.34520788 + 0.25 t = 2.34520788 + 0.25 Combine like terms: 2.34520788 + 0.25 = 2.59520788 t = 2.59520788 Simplifying t = 2.59520788Subproblem 2
t + -0.25 = -2.34520788 Simplifying t + -0.25 = -2.34520788 Reorder the terms: -0.25 + t = -2.34520788 Solving -0.25 + t = -2.34520788 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = -2.34520788 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -2.34520788 + 0.25 t = -2.34520788 + 0.25 Combine like terms: -2.34520788 + 0.25 = -2.09520788 t = -2.09520788 Simplifying t = -2.09520788Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.59520788, -2.09520788}
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