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Simplifying -16t2 + 72t + 5 = 0 Reorder the terms: 5 + 72t + -16t2 = 0 Solving 5 + 72t + -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'. -0.3125 + -4.5t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -4.5t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -4.5t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -4.5t + t2 = 0 + 0.3125 -4.5t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -4.5t + t2 = 0.3125 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 = 0.3125 + 5.0625 Reorder the terms: 5.0625 + -4.5t + t2 = 0.3125 + 5.0625 Combine like terms: 0.3125 + 5.0625 = 5.375 5.0625 + -4.5t + t2 = 5.375 Factor a perfect square on the left side: (t + -2.25)(t + -2.25) = 5.375 Calculate the square root of the right side: 2.318404624 Break this problem into two subproblems by setting (t + -2.25) equal to 2.318404624 and -2.318404624.Subproblem 1
t + -2.25 = 2.318404624 Simplifying t + -2.25 = 2.318404624 Reorder the terms: -2.25 + t = 2.318404624 Solving -2.25 + t = 2.318404624 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 = 2.318404624 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = 2.318404624 + 2.25 t = 2.318404624 + 2.25 Combine like terms: 2.318404624 + 2.25 = 4.568404624 t = 4.568404624 Simplifying t = 4.568404624Subproblem 2
t + -2.25 = -2.318404624 Simplifying t + -2.25 = -2.318404624 Reorder the terms: -2.25 + t = -2.318404624 Solving -2.25 + t = -2.318404624 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 = -2.318404624 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = -2.318404624 + 2.25 t = -2.318404624 + 2.25 Combine like terms: -2.318404624 + 2.25 = -0.068404624 t = -0.068404624 Simplifying t = -0.068404624Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.568404624, -0.068404624}
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