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Simplifying -16t2 + -22t + 425 = 0 Reorder the terms: 425 + -22t + -16t2 = 0 Solving 425 + -22t + -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'. -26.5625 + 1.375t + t2 = 0 Move the constant term to the right: Add '26.5625' to each side of the equation. -26.5625 + 1.375t + 26.5625 + t2 = 0 + 26.5625 Reorder the terms: -26.5625 + 26.5625 + 1.375t + t2 = 0 + 26.5625 Combine like terms: -26.5625 + 26.5625 = 0.0000 0.0000 + 1.375t + t2 = 0 + 26.5625 1.375t + t2 = 0 + 26.5625 Combine like terms: 0 + 26.5625 = 26.5625 1.375t + t2 = 26.5625 The t term is 1.375t. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375t + 0.47265625 + t2 = 26.5625 + 0.47265625 Reorder the terms: 0.47265625 + 1.375t + t2 = 26.5625 + 0.47265625 Combine like terms: 26.5625 + 0.47265625 = 27.03515625 0.47265625 + 1.375t + t2 = 27.03515625 Factor a perfect square on the left side: (t + 0.6875)(t + 0.6875) = 27.03515625 Calculate the square root of the right side: 5.199534234 Break this problem into two subproblems by setting (t + 0.6875) equal to 5.199534234 and -5.199534234.Subproblem 1
t + 0.6875 = 5.199534234 Simplifying t + 0.6875 = 5.199534234 Reorder the terms: 0.6875 + t = 5.199534234 Solving 0.6875 + t = 5.199534234 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + t = 5.199534234 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + t = 5.199534234 + -0.6875 t = 5.199534234 + -0.6875 Combine like terms: 5.199534234 + -0.6875 = 4.512034234 t = 4.512034234 Simplifying t = 4.512034234Subproblem 2
t + 0.6875 = -5.199534234 Simplifying t + 0.6875 = -5.199534234 Reorder the terms: 0.6875 + t = -5.199534234 Solving 0.6875 + t = -5.199534234 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + t = -5.199534234 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + t = -5.199534234 + -0.6875 t = -5.199534234 + -0.6875 Combine like terms: -5.199534234 + -0.6875 = -5.887034234 t = -5.887034234 Simplifying t = -5.887034234Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.512034234, -5.887034234}
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