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Simplifying 155 = 55.68t + 5t2 Solving 155 = 55.68t + 5t2 Solving for variable 't'. Reorder the terms: 155 + -55.68t + -5t2 = 55.68t + -55.68t + 5t2 + -5t2 Combine like terms: 55.68t + -55.68t = 0.00 155 + -55.68t + -5t2 = 0.00 + 5t2 + -5t2 155 + -55.68t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 155 + -55.68t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -31 + 11.136t + t2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + 11.136t + 31 + t2 = 0 + 31 Reorder the terms: -31 + 31 + 11.136t + t2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 11.136t + t2 = 0 + 31 11.136t + t2 = 0 + 31 Combine like terms: 0 + 31 = 31 11.136t + t2 = 31 The t term is 11.136t. Take half its coefficient (5.568). Square it (31.002624) and add it to both sides. Add '31.002624' to each side of the equation. 11.136t + 31.002624 + t2 = 31 + 31.002624 Reorder the terms: 31.002624 + 11.136t + t2 = 31 + 31.002624 Combine like terms: 31 + 31.002624 = 62.002624 31.002624 + 11.136t + t2 = 62.002624 Factor a perfect square on the left side: (t + 5.568)(t + 5.568) = 62.002624 Calculate the square root of the right side: 7.874174496 Break this problem into two subproblems by setting (t + 5.568) equal to 7.874174496 and -7.874174496.Subproblem 1
t + 5.568 = 7.874174496 Simplifying t + 5.568 = 7.874174496 Reorder the terms: 5.568 + t = 7.874174496 Solving 5.568 + t = 7.874174496 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.568' to each side of the equation. 5.568 + -5.568 + t = 7.874174496 + -5.568 Combine like terms: 5.568 + -5.568 = 0.000 0.000 + t = 7.874174496 + -5.568 t = 7.874174496 + -5.568 Combine like terms: 7.874174496 + -5.568 = 2.306174496 t = 2.306174496 Simplifying t = 2.306174496Subproblem 2
t + 5.568 = -7.874174496 Simplifying t + 5.568 = -7.874174496 Reorder the terms: 5.568 + t = -7.874174496 Solving 5.568 + t = -7.874174496 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.568' to each side of the equation. 5.568 + -5.568 + t = -7.874174496 + -5.568 Combine like terms: 5.568 + -5.568 = 0.000 0.000 + t = -7.874174496 + -5.568 t = -7.874174496 + -5.568 Combine like terms: -7.874174496 + -5.568 = -13.442174496 t = -13.442174496 Simplifying t = -13.442174496Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.306174496, -13.442174496}
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