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Simplifying 8t2 + 35t + -16 = 0 Reorder the terms: -16 + 35t + 8t2 = 0 Solving -16 + 35t + 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'. -2 + 4.375t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 4.375t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + 4.375t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4.375t + t2 = 0 + 2 4.375t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 4.375t + t2 = 2 The t term is 4.375t. Take half its coefficient (2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. 4.375t + 4.78515625 + t2 = 2 + 4.78515625 Reorder the terms: 4.78515625 + 4.375t + t2 = 2 + 4.78515625 Combine like terms: 2 + 4.78515625 = 6.78515625 4.78515625 + 4.375t + t2 = 6.78515625 Factor a perfect square on the left side: (t + 2.1875)(t + 2.1875) = 6.78515625 Calculate the square root of the right side: 2.604833248 Break this problem into two subproblems by setting (t + 2.1875) equal to 2.604833248 and -2.604833248.Subproblem 1
t + 2.1875 = 2.604833248 Simplifying t + 2.1875 = 2.604833248 Reorder the terms: 2.1875 + t = 2.604833248 Solving 2.1875 + t = 2.604833248 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.1875' to each side of the equation. 2.1875 + -2.1875 + t = 2.604833248 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + t = 2.604833248 + -2.1875 t = 2.604833248 + -2.1875 Combine like terms: 2.604833248 + -2.1875 = 0.417333248 t = 0.417333248 Simplifying t = 0.417333248Subproblem 2
t + 2.1875 = -2.604833248 Simplifying t + 2.1875 = -2.604833248 Reorder the terms: 2.1875 + t = -2.604833248 Solving 2.1875 + t = -2.604833248 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.1875' to each side of the equation. 2.1875 + -2.1875 + t = -2.604833248 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + t = -2.604833248 + -2.1875 t = -2.604833248 + -2.1875 Combine like terms: -2.604833248 + -2.1875 = -4.792333248 t = -4.792333248 Simplifying t = -4.792333248Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.417333248, -4.792333248}
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