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Simplifying -16t2 + 802.9567276t + 1.5 = 0 Reorder the terms: 1.5 + 802.9567276t + -16t2 = 0 Solving 1.5 + 802.9567276t + -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'. -0.09375 + -50.18479548t + t2 = 0 Move the constant term to the right: Add '0.09375' to each side of the equation. -0.09375 + -50.18479548t + 0.09375 + t2 = 0 + 0.09375 Reorder the terms: -0.09375 + 0.09375 + -50.18479548t + t2 = 0 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + -50.18479548t + t2 = 0 + 0.09375 -50.18479548t + t2 = 0 + 0.09375 Combine like terms: 0 + 0.09375 = 0.09375 -50.18479548t + t2 = 0.09375 The t term is -50.18479548t. Take half its coefficient (-25.09239774). Square it (629.6284243) and add it to both sides. Add '629.6284243' to each side of the equation. -50.18479548t + 629.6284243 + t2 = 0.09375 + 629.6284243 Reorder the terms: 629.6284243 + -50.18479548t + t2 = 0.09375 + 629.6284243 Combine like terms: 0.09375 + 629.6284243 = 629.7221743 629.6284243 + -50.18479548t + t2 = 629.7221743 Factor a perfect square on the left side: (t + -25.09239774)(t + -25.09239774) = 629.7221743 Calculate the square root of the right side: 25.094265765 Break this problem into two subproblems by setting (t + -25.09239774) equal to 25.094265765 and -25.094265765.Subproblem 1
t + -25.09239774 = 25.094265765 Simplifying t + -25.09239774 = 25.094265765 Reorder the terms: -25.09239774 + t = 25.094265765 Solving -25.09239774 + t = 25.094265765 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25.09239774' to each side of the equation. -25.09239774 + 25.09239774 + t = 25.094265765 + 25.09239774 Combine like terms: -25.09239774 + 25.09239774 = 0.00000000 0.00000000 + t = 25.094265765 + 25.09239774 t = 25.094265765 + 25.09239774 Combine like terms: 25.094265765 + 25.09239774 = 50.186663505 t = 50.186663505 Simplifying t = 50.186663505Subproblem 2
t + -25.09239774 = -25.094265765 Simplifying t + -25.09239774 = -25.094265765 Reorder the terms: -25.09239774 + t = -25.094265765 Solving -25.09239774 + t = -25.094265765 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25.09239774' to each side of the equation. -25.09239774 + 25.09239774 + t = -25.094265765 + 25.09239774 Combine like terms: -25.09239774 + 25.09239774 = 0.00000000 0.00000000 + t = -25.094265765 + 25.09239774 t = -25.094265765 + 25.09239774 Combine like terms: -25.094265765 + 25.09239774 = -0.001868025 t = -0.001868025 Simplifying t = -0.001868025Solution
The solution to the problem is based on the solutions from the subproblems. t = {50.186663505, -0.001868025}
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