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Simplifying 16t2 + -72t + -3 = 84 Reorder the terms: -3 + -72t + 16t2 = 84 Solving -3 + -72t + 16t2 = 84 Solving for variable 't'. Reorder the terms: -3 + -84 + -72t + 16t2 = 84 + -84 Combine like terms: -3 + -84 = -87 -87 + -72t + 16t2 = 84 + -84 Combine like terms: 84 + -84 = 0 -87 + -72t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -5.4375 + -4.5t + t2 = 0 Move the constant term to the right: Add '5.4375' to each side of the equation. -5.4375 + -4.5t + 5.4375 + t2 = 0 + 5.4375 Reorder the terms: -5.4375 + 5.4375 + -4.5t + t2 = 0 + 5.4375 Combine like terms: -5.4375 + 5.4375 = 0.0000 0.0000 + -4.5t + t2 = 0 + 5.4375 -4.5t + t2 = 0 + 5.4375 Combine like terms: 0 + 5.4375 = 5.4375 -4.5t + t2 = 5.4375 The t term is -4.5t. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5t + 5.0625 + t2 = 5.4375 + 5.0625 Reorder the terms: 5.0625 + -4.5t + t2 = 5.4375 + 5.0625 Combine like terms: 5.4375 + 5.0625 = 10.5 5.0625 + -4.5t + t2 = 10.5 Factor a perfect square on the left side: (t + -2.25)(t + -2.25) = 10.5 Calculate the square root of the right side: 3.240370349 Break this problem into two subproblems by setting (t + -2.25) equal to 3.240370349 and -3.240370349.Subproblem 1
t + -2.25 = 3.240370349 Simplifying t + -2.25 = 3.240370349 Reorder the terms: -2.25 + t = 3.240370349 Solving -2.25 + t = 3.240370349 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = 3.240370349 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = 3.240370349 + 2.25 t = 3.240370349 + 2.25 Combine like terms: 3.240370349 + 2.25 = 5.490370349 t = 5.490370349 Simplifying t = 5.490370349Subproblem 2
t + -2.25 = -3.240370349 Simplifying t + -2.25 = -3.240370349 Reorder the terms: -2.25 + t = -3.240370349 Solving -2.25 + t = -3.240370349 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = -3.240370349 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = -3.240370349 + 2.25 t = -3.240370349 + 2.25 Combine like terms: -3.240370349 + 2.25 = -0.990370349 t = -0.990370349 Simplifying t = -0.990370349Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.490370349, -0.990370349}
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