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Simplifying -8t2 + 63t + 2 = 0 Reorder the terms: 2 + 63t + -8t2 = 0 Solving 2 + 63t + -8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.25 + -7.875t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -7.875t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -7.875t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -7.875t + t2 = 0 + 0.25 -7.875t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -7.875t + t2 = 0.25 The t term is -7.875t. Take half its coefficient (-3.9375). Square it (15.50390625) and add it to both sides. Add '15.50390625' to each side of the equation. -7.875t + 15.50390625 + t2 = 0.25 + 15.50390625 Reorder the terms: 15.50390625 + -7.875t + t2 = 0.25 + 15.50390625 Combine like terms: 0.25 + 15.50390625 = 15.75390625 15.50390625 + -7.875t + t2 = 15.75390625 Factor a perfect square on the left side: (t + -3.9375)(t + -3.9375) = 15.75390625 Calculate the square root of the right side: 3.969119077 Break this problem into two subproblems by setting (t + -3.9375) equal to 3.969119077 and -3.969119077.Subproblem 1
t + -3.9375 = 3.969119077 Simplifying t + -3.9375 = 3.969119077 Reorder the terms: -3.9375 + t = 3.969119077 Solving -3.9375 + t = 3.969119077 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.9375' to each side of the equation. -3.9375 + 3.9375 + t = 3.969119077 + 3.9375 Combine like terms: -3.9375 + 3.9375 = 0.0000 0.0000 + t = 3.969119077 + 3.9375 t = 3.969119077 + 3.9375 Combine like terms: 3.969119077 + 3.9375 = 7.906619077 t = 7.906619077 Simplifying t = 7.906619077Subproblem 2
t + -3.9375 = -3.969119077 Simplifying t + -3.9375 = -3.969119077 Reorder the terms: -3.9375 + t = -3.969119077 Solving -3.9375 + t = -3.969119077 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.9375' to each side of the equation. -3.9375 + 3.9375 + t = -3.969119077 + 3.9375 Combine like terms: -3.9375 + 3.9375 = 0.0000 0.0000 + t = -3.969119077 + 3.9375 t = -3.969119077 + 3.9375 Combine like terms: -3.969119077 + 3.9375 = -0.031619077 t = -0.031619077 Simplifying t = -0.031619077Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.906619077, -0.031619077}
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