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Simplifying 0 = 3t2 + -6t + -5010 Reorder the terms: 0 = -5010 + -6t + 3t2 Solving 0 = -5010 + -6t + 3t2 Solving for variable 't'. Combine like terms: 0 + 5010 = 5010 5010 + 6t + -3t2 = -5010 + -6t + 3t2 + 5010 + 6t + -3t2 Reorder the terms: 5010 + 6t + -3t2 = -5010 + 5010 + -6t + 6t + 3t2 + -3t2 Combine like terms: -5010 + 5010 = 0 5010 + 6t + -3t2 = 0 + -6t + 6t + 3t2 + -3t2 5010 + 6t + -3t2 = -6t + 6t + 3t2 + -3t2 Combine like terms: -6t + 6t = 0 5010 + 6t + -3t2 = 0 + 3t2 + -3t2 5010 + 6t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 5010 + 6t + -3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1670 + 2t + -1t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1670 + 2t + -1t2)' equal to zero and attempt to solve: Simplifying 1670 + 2t + -1t2 = 0 Solving 1670 + 2t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1670 + -2t + t2 = 0 Move the constant term to the right: Add '1670' to each side of the equation. -1670 + -2t + 1670 + t2 = 0 + 1670 Reorder the terms: -1670 + 1670 + -2t + t2 = 0 + 1670 Combine like terms: -1670 + 1670 = 0 0 + -2t + t2 = 0 + 1670 -2t + t2 = 0 + 1670 Combine like terms: 0 + 1670 = 1670 -2t + t2 = 1670 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 1670 + 1 Reorder the terms: 1 + -2t + t2 = 1670 + 1 Combine like terms: 1670 + 1 = 1671 1 + -2t + t2 = 1671 Factor a perfect square on the left side: (t + -1)(t + -1) = 1671 Calculate the square root of the right side: 40.877866872 Break this problem into two subproblems by setting (t + -1) equal to 40.877866872 and -40.877866872.Subproblem 1
t + -1 = 40.877866872 Simplifying t + -1 = 40.877866872 Reorder the terms: -1 + t = 40.877866872 Solving -1 + t = 40.877866872 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 40.877866872 + 1 Combine like terms: -1 + 1 = 0 0 + t = 40.877866872 + 1 t = 40.877866872 + 1 Combine like terms: 40.877866872 + 1 = 41.877866872 t = 41.877866872 Simplifying t = 41.877866872Subproblem 2
t + -1 = -40.877866872 Simplifying t + -1 = -40.877866872 Reorder the terms: -1 + t = -40.877866872 Solving -1 + t = -40.877866872 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -40.877866872 + 1 Combine like terms: -1 + 1 = 0 0 + t = -40.877866872 + 1 t = -40.877866872 + 1 Combine like terms: -40.877866872 + 1 = -39.877866872 t = -39.877866872 Simplifying t = -39.877866872Solution
The solution to the problem is based on the solutions from the subproblems. t = {41.877866872, -39.877866872}Solution
t = {41.877866872, -39.877866872}
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