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Simplifying 16t2 + -175t + 8 = 0 Reorder the terms: 8 + -175t + 16t2 = 0 Solving 8 + -175t + 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'. 0.5 + -10.9375t + t2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -10.9375t + -0.5 + t2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -10.9375t + t2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -10.9375t + t2 = 0 + -0.5 -10.9375t + t2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -10.9375t + t2 = -0.5 The t term is -10.9375t. Take half its coefficient (-5.46875). Square it (29.90722656) and add it to both sides. Add '29.90722656' to each side of the equation. -10.9375t + 29.90722656 + t2 = -0.5 + 29.90722656 Reorder the terms: 29.90722656 + -10.9375t + t2 = -0.5 + 29.90722656 Combine like terms: -0.5 + 29.90722656 = 29.40722656 29.90722656 + -10.9375t + t2 = 29.40722656 Factor a perfect square on the left side: (t + -5.46875)(t + -5.46875) = 29.40722656 Calculate the square root of the right side: 5.422843033 Break this problem into two subproblems by setting (t + -5.46875) equal to 5.422843033 and -5.422843033.Subproblem 1
t + -5.46875 = 5.422843033 Simplifying t + -5.46875 = 5.422843033 Reorder the terms: -5.46875 + t = 5.422843033 Solving -5.46875 + t = 5.422843033 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.46875' to each side of the equation. -5.46875 + 5.46875 + t = 5.422843033 + 5.46875 Combine like terms: -5.46875 + 5.46875 = 0.00000 0.00000 + t = 5.422843033 + 5.46875 t = 5.422843033 + 5.46875 Combine like terms: 5.422843033 + 5.46875 = 10.891593033 t = 10.891593033 Simplifying t = 10.891593033Subproblem 2
t + -5.46875 = -5.422843033 Simplifying t + -5.46875 = -5.422843033 Reorder the terms: -5.46875 + t = -5.422843033 Solving -5.46875 + t = -5.422843033 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.46875' to each side of the equation. -5.46875 + 5.46875 + t = -5.422843033 + 5.46875 Combine like terms: -5.46875 + 5.46875 = 0.00000 0.00000 + t = -5.422843033 + 5.46875 t = -5.422843033 + 5.46875 Combine like terms: -5.422843033 + 5.46875 = 0.045906967 t = 0.045906967 Simplifying t = 0.045906967Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.891593033, 0.045906967}
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