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Simplifying -25 = -16t2 + 72t Reorder the terms: -25 = 72t + -16t2 Solving -25 = 72t + -16t2 Solving for variable 't'. Reorder the terms: -25 + -72t + 16t2 = 72t + -72t + -16t2 + 16t2 Combine like terms: 72t + -72t = 0 -25 + -72t + 16t2 = 0 + -16t2 + 16t2 -25 + -72t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -25 + -72t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + -4.5t + t2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + -4.5t + 1.5625 + t2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + -4.5t + t2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + -4.5t + t2 = 0 + 1.5625 -4.5t + t2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 -4.5t + t2 = 1.5625 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 = 1.5625 + 5.0625 Reorder the terms: 5.0625 + -4.5t + t2 = 1.5625 + 5.0625 Combine like terms: 1.5625 + 5.0625 = 6.625 5.0625 + -4.5t + t2 = 6.625 Factor a perfect square on the left side: (t + -2.25)(t + -2.25) = 6.625 Calculate the square root of the right side: 2.573907535 Break this problem into two subproblems by setting (t + -2.25) equal to 2.573907535 and -2.573907535.Subproblem 1
t + -2.25 = 2.573907535 Simplifying t + -2.25 = 2.573907535 Reorder the terms: -2.25 + t = 2.573907535 Solving -2.25 + t = 2.573907535 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 = 2.573907535 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = 2.573907535 + 2.25 t = 2.573907535 + 2.25 Combine like terms: 2.573907535 + 2.25 = 4.823907535 t = 4.823907535 Simplifying t = 4.823907535Subproblem 2
t + -2.25 = -2.573907535 Simplifying t + -2.25 = -2.573907535 Reorder the terms: -2.25 + t = -2.573907535 Solving -2.25 + t = -2.573907535 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 = -2.573907535 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = -2.573907535 + 2.25 t = -2.573907535 + 2.25 Combine like terms: -2.573907535 + 2.25 = -0.323907535 t = -0.323907535 Simplifying t = -0.323907535Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.823907535, -0.323907535}
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