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Simplifying 15t2 + -16t + -30 = 0 Reorder the terms: -30 + -16t + 15t2 = 0 Solving -30 + -16t + 15t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -2 + -1.066666667t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.066666667t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -1.066666667t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.066666667t + t2 = 0 + 2 -1.066666667t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.066666667t + t2 = 2 The t term is -1.066666667t. Take half its coefficient (-0.5333333335). Square it (0.2844444446) and add it to both sides. Add '0.2844444446' to each side of the equation. -1.066666667t + 0.2844444446 + t2 = 2 + 0.2844444446 Reorder the terms: 0.2844444446 + -1.066666667t + t2 = 2 + 0.2844444446 Combine like terms: 2 + 0.2844444446 = 2.2844444446 0.2844444446 + -1.066666667t + t2 = 2.2844444446 Factor a perfect square on the left side: (t + -0.5333333335)(t + -0.5333333335) = 2.2844444446 Calculate the square root of the right side: 1.511437873 Break this problem into two subproblems by setting (t + -0.5333333335) equal to 1.511437873 and -1.511437873.Subproblem 1
t + -0.5333333335 = 1.511437873 Simplifying t + -0.5333333335 = 1.511437873 Reorder the terms: -0.5333333335 + t = 1.511437873 Solving -0.5333333335 + t = 1.511437873 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5333333335' to each side of the equation. -0.5333333335 + 0.5333333335 + t = 1.511437873 + 0.5333333335 Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000 0.0000000000 + t = 1.511437873 + 0.5333333335 t = 1.511437873 + 0.5333333335 Combine like terms: 1.511437873 + 0.5333333335 = 2.0447712065 t = 2.0447712065 Simplifying t = 2.0447712065Subproblem 2
t + -0.5333333335 = -1.511437873 Simplifying t + -0.5333333335 = -1.511437873 Reorder the terms: -0.5333333335 + t = -1.511437873 Solving -0.5333333335 + t = -1.511437873 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5333333335' to each side of the equation. -0.5333333335 + 0.5333333335 + t = -1.511437873 + 0.5333333335 Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000 0.0000000000 + t = -1.511437873 + 0.5333333335 t = -1.511437873 + 0.5333333335 Combine like terms: -1.511437873 + 0.5333333335 = -0.9781045395 t = -0.9781045395 Simplifying t = -0.9781045395Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.0447712065, -0.9781045395}
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