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Simplifying 0 = 6t2 + 63t + 4 Reorder the terms: 0 = 4 + 63t + 6t2 Solving 0 = 4 + 63t + 6t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -63t + -6t2 = 4 + 63t + 6t2 + -4 + -63t + -6t2 Reorder the terms: -4 + -63t + -6t2 = 4 + -4 + 63t + -63t + 6t2 + -6t2 Combine like terms: 4 + -4 = 0 -4 + -63t + -6t2 = 0 + 63t + -63t + 6t2 + -6t2 -4 + -63t + -6t2 = 63t + -63t + 6t2 + -6t2 Combine like terms: 63t + -63t = 0 -4 + -63t + -6t2 = 0 + 6t2 + -6t2 -4 + -63t + -6t2 = 6t2 + -6t2 Combine like terms: 6t2 + -6t2 = 0 -4 + -63t + -6t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 63t + 6t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 63t + 6t2)' equal to zero and attempt to solve: Simplifying 4 + 63t + 6t2 = 0 Solving 4 + 63t + 6t2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.6666666667 + 10.5t + t2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 10.5t + -0.6666666667 + t2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 10.5t + t2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 10.5t + t2 = 0 + -0.6666666667 10.5t + t2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 10.5t + t2 = -0.6666666667 The t term is 10.5t. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5t + 27.5625 + t2 = -0.6666666667 + 27.5625 Reorder the terms: 27.5625 + 10.5t + t2 = -0.6666666667 + 27.5625 Combine like terms: -0.6666666667 + 27.5625 = 26.8958333333 27.5625 + 10.5t + t2 = 26.8958333333 Factor a perfect square on the left side: (t + 5.25)(t + 5.25) = 26.8958333333 Calculate the square root of the right side: 5.186119294 Break this problem into two subproblems by setting (t + 5.25) equal to 5.186119294 and -5.186119294.Subproblem 1
t + 5.25 = 5.186119294 Simplifying t + 5.25 = 5.186119294 Reorder the terms: 5.25 + t = 5.186119294 Solving 5.25 + t = 5.186119294 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + t = 5.186119294 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + t = 5.186119294 + -5.25 t = 5.186119294 + -5.25 Combine like terms: 5.186119294 + -5.25 = -0.063880706 t = -0.063880706 Simplifying t = -0.063880706Subproblem 2
t + 5.25 = -5.186119294 Simplifying t + 5.25 = -5.186119294 Reorder the terms: 5.25 + t = -5.186119294 Solving 5.25 + t = -5.186119294 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + t = -5.186119294 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + t = -5.186119294 + -5.25 t = -5.186119294 + -5.25 Combine like terms: -5.186119294 + -5.25 = -10.436119294 t = -10.436119294 Simplifying t = -10.436119294Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.063880706, -10.436119294}Solution
t = {-0.063880706, -10.436119294}
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