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Simplifying -16t2 + 75t + 6 = 0 Reorder the terms: 6 + 75t + -16t2 = 0 Solving 6 + 75t + -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'. -0.375 + -4.6875t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -4.6875t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -4.6875t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -4.6875t + t2 = 0 + 0.375 -4.6875t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -4.6875t + t2 = 0.375 The t term is -4.6875t. Take half its coefficient (-2.34375). Square it (5.493164063) and add it to both sides. Add '5.493164063' to each side of the equation. -4.6875t + 5.493164063 + t2 = 0.375 + 5.493164063 Reorder the terms: 5.493164063 + -4.6875t + t2 = 0.375 + 5.493164063 Combine like terms: 0.375 + 5.493164063 = 5.868164063 5.493164063 + -4.6875t + t2 = 5.868164063 Factor a perfect square on the left side: (t + -2.34375)(t + -2.34375) = 5.868164063 Calculate the square root of the right side: 2.422429372 Break this problem into two subproblems by setting (t + -2.34375) equal to 2.422429372 and -2.422429372.Subproblem 1
t + -2.34375 = 2.422429372 Simplifying t + -2.34375 = 2.422429372 Reorder the terms: -2.34375 + t = 2.422429372 Solving -2.34375 + t = 2.422429372 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + t = 2.422429372 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + t = 2.422429372 + 2.34375 t = 2.422429372 + 2.34375 Combine like terms: 2.422429372 + 2.34375 = 4.766179372 t = 4.766179372 Simplifying t = 4.766179372Subproblem 2
t + -2.34375 = -2.422429372 Simplifying t + -2.34375 = -2.422429372 Reorder the terms: -2.34375 + t = -2.422429372 Solving -2.34375 + t = -2.422429372 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + t = -2.422429372 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + t = -2.422429372 + 2.34375 t = -2.422429372 + 2.34375 Combine like terms: -2.422429372 + 2.34375 = -0.078679372 t = -0.078679372 Simplifying t = -0.078679372Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.766179372, -0.078679372}
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