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Simplifying -16t2 + 141t + 58 = 0 Reorder the terms: 58 + 141t + -16t2 = 0 Solving 58 + 141t + -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'. -3.625 + -8.8125t + t2 = 0 Move the constant term to the right: Add '3.625' to each side of the equation. -3.625 + -8.8125t + 3.625 + t2 = 0 + 3.625 Reorder the terms: -3.625 + 3.625 + -8.8125t + t2 = 0 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + -8.8125t + t2 = 0 + 3.625 -8.8125t + t2 = 0 + 3.625 Combine like terms: 0 + 3.625 = 3.625 -8.8125t + t2 = 3.625 The t term is -8.8125t. Take half its coefficient (-4.40625). Square it (19.41503906) and add it to both sides. Add '19.41503906' to each side of the equation. -8.8125t + 19.41503906 + t2 = 3.625 + 19.41503906 Reorder the terms: 19.41503906 + -8.8125t + t2 = 3.625 + 19.41503906 Combine like terms: 3.625 + 19.41503906 = 23.04003906 19.41503906 + -8.8125t + t2 = 23.04003906 Factor a perfect square on the left side: (t + -4.40625)(t + -4.40625) = 23.04003906 Calculate the square root of the right side: 4.800004069 Break this problem into two subproblems by setting (t + -4.40625) equal to 4.800004069 and -4.800004069.Subproblem 1
t + -4.40625 = 4.800004069 Simplifying t + -4.40625 = 4.800004069 Reorder the terms: -4.40625 + t = 4.800004069 Solving -4.40625 + t = 4.800004069 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.40625' to each side of the equation. -4.40625 + 4.40625 + t = 4.800004069 + 4.40625 Combine like terms: -4.40625 + 4.40625 = 0.00000 0.00000 + t = 4.800004069 + 4.40625 t = 4.800004069 + 4.40625 Combine like terms: 4.800004069 + 4.40625 = 9.206254069 t = 9.206254069 Simplifying t = 9.206254069Subproblem 2
t + -4.40625 = -4.800004069 Simplifying t + -4.40625 = -4.800004069 Reorder the terms: -4.40625 + t = -4.800004069 Solving -4.40625 + t = -4.800004069 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.40625' to each side of the equation. -4.40625 + 4.40625 + t = -4.800004069 + 4.40625 Combine like terms: -4.40625 + 4.40625 = 0.00000 0.00000 + t = -4.800004069 + 4.40625 t = -4.800004069 + 4.40625 Combine like terms: -4.800004069 + 4.40625 = -0.393754069 t = -0.393754069 Simplifying t = -0.393754069Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.206254069, -0.393754069}
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