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Simplifying 16t2 + -151t = 88 Reorder the terms: -151t + 16t2 = 88 Solving -151t + 16t2 = 88 Solving for variable 't'. Reorder the terms: -88 + -151t + 16t2 = 88 + -88 Combine like terms: 88 + -88 = 0 -88 + -151t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -5.5 + -9.4375t + t2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -9.4375t + 5.5 + t2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -9.4375t + t2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -9.4375t + t2 = 0 + 5.5 -9.4375t + t2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -9.4375t + t2 = 5.5 The t term is -9.4375t. Take half its coefficient (-4.71875). Square it (22.26660156) and add it to both sides. Add '22.26660156' to each side of the equation. -9.4375t + 22.26660156 + t2 = 5.5 + 22.26660156 Reorder the terms: 22.26660156 + -9.4375t + t2 = 5.5 + 22.26660156 Combine like terms: 5.5 + 22.26660156 = 27.76660156 22.26660156 + -9.4375t + t2 = 27.76660156 Factor a perfect square on the left side: (t + -4.71875)(t + -4.71875) = 27.76660156 Calculate the square root of the right side: 5.269402391 Break this problem into two subproblems by setting (t + -4.71875) equal to 5.269402391 and -5.269402391.Subproblem 1
t + -4.71875 = 5.269402391 Simplifying t + -4.71875 = 5.269402391 Reorder the terms: -4.71875 + t = 5.269402391 Solving -4.71875 + t = 5.269402391 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.71875' to each side of the equation. -4.71875 + 4.71875 + t = 5.269402391 + 4.71875 Combine like terms: -4.71875 + 4.71875 = 0.00000 0.00000 + t = 5.269402391 + 4.71875 t = 5.269402391 + 4.71875 Combine like terms: 5.269402391 + 4.71875 = 9.988152391 t = 9.988152391 Simplifying t = 9.988152391Subproblem 2
t + -4.71875 = -5.269402391 Simplifying t + -4.71875 = -5.269402391 Reorder the terms: -4.71875 + t = -5.269402391 Solving -4.71875 + t = -5.269402391 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.71875' to each side of the equation. -4.71875 + 4.71875 + t = -5.269402391 + 4.71875 Combine like terms: -4.71875 + 4.71875 = 0.00000 0.00000 + t = -5.269402391 + 4.71875 t = -5.269402391 + 4.71875 Combine like terms: -5.269402391 + 4.71875 = -0.550652391 t = -0.550652391 Simplifying t = -0.550652391Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.988152391, -0.550652391}
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