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Simplifying 0 = -16t2 + 351t + 126 Reorder the terms: 0 = 126 + 351t + -16t2 Solving 0 = 126 + 351t + -16t2 Solving for variable 't'. Combine like terms: 0 + -126 = -126 -126 + -351t + 16t2 = 126 + 351t + -16t2 + -126 + -351t + 16t2 Reorder the terms: -126 + -351t + 16t2 = 126 + -126 + 351t + -351t + -16t2 + 16t2 Combine like terms: 126 + -126 = 0 -126 + -351t + 16t2 = 0 + 351t + -351t + -16t2 + 16t2 -126 + -351t + 16t2 = 351t + -351t + -16t2 + 16t2 Combine like terms: 351t + -351t = 0 -126 + -351t + 16t2 = 0 + -16t2 + 16t2 -126 + -351t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -126 + -351t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -7.875 + -21.9375t + t2 = 0 Move the constant term to the right: Add '7.875' to each side of the equation. -7.875 + -21.9375t + 7.875 + t2 = 0 + 7.875 Reorder the terms: -7.875 + 7.875 + -21.9375t + t2 = 0 + 7.875 Combine like terms: -7.875 + 7.875 = 0.000 0.000 + -21.9375t + t2 = 0 + 7.875 -21.9375t + t2 = 0 + 7.875 Combine like terms: 0 + 7.875 = 7.875 -21.9375t + t2 = 7.875 The t term is -21.9375t. Take half its coefficient (-10.96875). Square it (120.3134766) and add it to both sides. Add '120.3134766' to each side of the equation. -21.9375t + 120.3134766 + t2 = 7.875 + 120.3134766 Reorder the terms: 120.3134766 + -21.9375t + t2 = 7.875 + 120.3134766 Combine like terms: 7.875 + 120.3134766 = 128.1884766 120.3134766 + -21.9375t + t2 = 128.1884766 Factor a perfect square on the left side: (t + -10.96875)(t + -10.96875) = 128.1884766 Calculate the square root of the right side: 11.322035003 Break this problem into two subproblems by setting (t + -10.96875) equal to 11.322035003 and -11.322035003.Subproblem 1
t + -10.96875 = 11.322035003 Simplifying t + -10.96875 = 11.322035003 Reorder the terms: -10.96875 + t = 11.322035003 Solving -10.96875 + t = 11.322035003 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10.96875' to each side of the equation. -10.96875 + 10.96875 + t = 11.322035003 + 10.96875 Combine like terms: -10.96875 + 10.96875 = 0.00000 0.00000 + t = 11.322035003 + 10.96875 t = 11.322035003 + 10.96875 Combine like terms: 11.322035003 + 10.96875 = 22.290785003 t = 22.290785003 Simplifying t = 22.290785003Subproblem 2
t + -10.96875 = -11.322035003 Simplifying t + -10.96875 = -11.322035003 Reorder the terms: -10.96875 + t = -11.322035003 Solving -10.96875 + t = -11.322035003 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10.96875' to each side of the equation. -10.96875 + 10.96875 + t = -11.322035003 + 10.96875 Combine like terms: -10.96875 + 10.96875 = 0.00000 0.00000 + t = -11.322035003 + 10.96875 t = -11.322035003 + 10.96875 Combine like terms: -11.322035003 + 10.96875 = -0.353285003 t = -0.353285003 Simplifying t = -0.353285003Solution
The solution to the problem is based on the solutions from the subproblems. t = {22.290785003, -0.353285003}
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