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Simplifying -16t2 + 8t + 9 = 0 Reorder the terms: 9 + 8t + -16t2 = 0 Solving 9 + 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'. -0.5625 + -0.5t + t2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + -0.5t + 0.5625 + t2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + -0.5t + t2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + -0.5t + t2 = 0 + 0.5625 -0.5t + t2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 -0.5t + t2 = 0.5625 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 = 0.5625 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 0.5625 + 0.0625 Combine like terms: 0.5625 + 0.0625 = 0.625 0.0625 + -0.5t + t2 = 0.625 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 0.625 Calculate the square root of the right side: 0.790569415 Break this problem into two subproblems by setting (t + -0.25) equal to 0.790569415 and -0.790569415.Subproblem 1
t + -0.25 = 0.790569415 Simplifying t + -0.25 = 0.790569415 Reorder the terms: -0.25 + t = 0.790569415 Solving -0.25 + t = 0.790569415 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 = 0.790569415 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 0.790569415 + 0.25 t = 0.790569415 + 0.25 Combine like terms: 0.790569415 + 0.25 = 1.040569415 t = 1.040569415 Simplifying t = 1.040569415Subproblem 2
t + -0.25 = -0.790569415 Simplifying t + -0.25 = -0.790569415 Reorder the terms: -0.25 + t = -0.790569415 Solving -0.25 + t = -0.790569415 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 = -0.790569415 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -0.790569415 + 0.25 t = -0.790569415 + 0.25 Combine like terms: -0.790569415 + 0.25 = -0.540569415 t = -0.540569415 Simplifying t = -0.540569415Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.040569415, -0.540569415}
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