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Simplifying 19.6728t2 + -156.792t + 126.02 = 0 Reorder the terms: 126.02 + -156.792t + 19.6728t2 = 0 Solving 126.02 + -156.792t + 19.6728t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 19.6728 the coefficient of the squared term: Divide each side by '19.6728'. 6.40579887 + -7.96998902t + t2 = 0 Move the constant term to the right: Add '-6.40579887' to each side of the equation. 6.40579887 + -7.96998902t + -6.40579887 + t2 = 0 + -6.40579887 Reorder the terms: 6.40579887 + -6.40579887 + -7.96998902t + t2 = 0 + -6.40579887 Combine like terms: 6.40579887 + -6.40579887 = 0.00000000 0.00000000 + -7.96998902t + t2 = 0 + -6.40579887 -7.96998902t + t2 = 0 + -6.40579887 Combine like terms: 0 + -6.40579887 = -6.40579887 -7.96998902t + t2 = -6.40579887 The t term is -7.96998902t. Take half its coefficient (-3.98499451). Square it (15.88018124) and add it to both sides. Add '15.88018124' to each side of the equation. -7.96998902t + 15.88018124 + t2 = -6.40579887 + 15.88018124 Reorder the terms: 15.88018124 + -7.96998902t + t2 = -6.40579887 + 15.88018124 Combine like terms: -6.40579887 + 15.88018124 = 9.47438237 15.88018124 + -7.96998902t + t2 = 9.47438237 Factor a perfect square on the left side: (t + -3.98499451)(t + -3.98499451) = 9.47438237 Calculate the square root of the right side: 3.078048468 Break this problem into two subproblems by setting (t + -3.98499451) equal to 3.078048468 and -3.078048468.Subproblem 1
t + -3.98499451 = 3.078048468 Simplifying t + -3.98499451 = 3.078048468 Reorder the terms: -3.98499451 + t = 3.078048468 Solving -3.98499451 + t = 3.078048468 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.98499451' to each side of the equation. -3.98499451 + 3.98499451 + t = 3.078048468 + 3.98499451 Combine like terms: -3.98499451 + 3.98499451 = 0.00000000 0.00000000 + t = 3.078048468 + 3.98499451 t = 3.078048468 + 3.98499451 Combine like terms: 3.078048468 + 3.98499451 = 7.063042978 t = 7.063042978 Simplifying t = 7.063042978Subproblem 2
t + -3.98499451 = -3.078048468 Simplifying t + -3.98499451 = -3.078048468 Reorder the terms: -3.98499451 + t = -3.078048468 Solving -3.98499451 + t = -3.078048468 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.98499451' to each side of the equation. -3.98499451 + 3.98499451 + t = -3.078048468 + 3.98499451 Combine like terms: -3.98499451 + 3.98499451 = 0.00000000 0.00000000 + t = -3.078048468 + 3.98499451 t = -3.078048468 + 3.98499451 Combine like terms: -3.078048468 + 3.98499451 = 0.906946042 t = 0.906946042 Simplifying t = 0.906946042Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.063042978, 0.906946042}
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