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Simplifying -16t2 + 175t + 500 = 0 Reorder the terms: 500 + 175t + -16t2 = 0 Solving 500 + 175t + -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'. -31.25 + -10.9375t + t2 = 0 Move the constant term to the right: Add '31.25' to each side of the equation. -31.25 + -10.9375t + 31.25 + t2 = 0 + 31.25 Reorder the terms: -31.25 + 31.25 + -10.9375t + t2 = 0 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + -10.9375t + t2 = 0 + 31.25 -10.9375t + t2 = 0 + 31.25 Combine like terms: 0 + 31.25 = 31.25 -10.9375t + t2 = 31.25 The t term is -10.9375t. Take half its coefficient (-5.46875). Square it (29.90722656) and add it to both sides. Add '29.90722656' to each side of the equation. -10.9375t + 29.90722656 + t2 = 31.25 + 29.90722656 Reorder the terms: 29.90722656 + -10.9375t + t2 = 31.25 + 29.90722656 Combine like terms: 31.25 + 29.90722656 = 61.15722656 29.90722656 + -10.9375t + t2 = 61.15722656 Factor a perfect square on the left side: (t + -5.46875)(t + -5.46875) = 61.15722656 Calculate the square root of the right side: 7.820308597 Break this problem into two subproblems by setting (t + -5.46875) equal to 7.820308597 and -7.820308597.Subproblem 1
t + -5.46875 = 7.820308597 Simplifying t + -5.46875 = 7.820308597 Reorder the terms: -5.46875 + t = 7.820308597 Solving -5.46875 + t = 7.820308597 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.46875' to each side of the equation. -5.46875 + 5.46875 + t = 7.820308597 + 5.46875 Combine like terms: -5.46875 + 5.46875 = 0.00000 0.00000 + t = 7.820308597 + 5.46875 t = 7.820308597 + 5.46875 Combine like terms: 7.820308597 + 5.46875 = 13.289058597 t = 13.289058597 Simplifying t = 13.289058597Subproblem 2
t + -5.46875 = -7.820308597 Simplifying t + -5.46875 = -7.820308597 Reorder the terms: -5.46875 + t = -7.820308597 Solving -5.46875 + t = -7.820308597 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.46875' to each side of the equation. -5.46875 + 5.46875 + t = -7.820308597 + 5.46875 Combine like terms: -5.46875 + 5.46875 = 0.00000 0.00000 + t = -7.820308597 + 5.46875 t = -7.820308597 + 5.46875 Combine like terms: -7.820308597 + 5.46875 = -2.351558597 t = -2.351558597 Simplifying t = -2.351558597Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.289058597, -2.351558597}
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