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Simplifying -3(2t + -5) * 22t = 5t + -4 Reorder the terms: -3(-5 + 2t) * 22t = 5t + -4 Reorder the terms for easier multiplication: -3 * 22t(-5 + 2t) = 5t + -4 Multiply -3 * 22 -66t(-5 + 2t) = 5t + -4 (-5 * -66t + 2t * -66t) = 5t + -4 (330t + -132t2) = 5t + -4 Reorder the terms: 330t + -132t2 = -4 + 5t Solving 330t + -132t2 = -4 + 5t Solving for variable 't'. Reorder the terms: 4 + 330t + -5t + -132t2 = -4 + 5t + 4 + -5t Combine like terms: 330t + -5t = 325t 4 + 325t + -132t2 = -4 + 5t + 4 + -5t Reorder the terms: 4 + 325t + -132t2 = -4 + 4 + 5t + -5t Combine like terms: -4 + 4 = 0 4 + 325t + -132t2 = 0 + 5t + -5t 4 + 325t + -132t2 = 5t + -5t Combine like terms: 5t + -5t = 0 4 + 325t + -132t2 = 0 Begin completing the square. Divide all terms by -132 the coefficient of the squared term: Divide each side by '-132'. -0.0303030303 + -2.462121212t + t2 = 0 Move the constant term to the right: Add '0.0303030303' to each side of the equation. -0.0303030303 + -2.462121212t + 0.0303030303 + t2 = 0 + 0.0303030303 Reorder the terms: -0.0303030303 + 0.0303030303 + -2.462121212t + t2 = 0 + 0.0303030303 Combine like terms: -0.0303030303 + 0.0303030303 = 0.0000000000 0.0000000000 + -2.462121212t + t2 = 0 + 0.0303030303 -2.462121212t + t2 = 0 + 0.0303030303 Combine like terms: 0 + 0.0303030303 = 0.0303030303 -2.462121212t + t2 = 0.0303030303 The t term is -2.462121212t. Take half its coefficient (-1.231060606). Square it (1.515510216) and add it to both sides. Add '1.515510216' to each side of the equation. -2.462121212t + 1.515510216 + t2 = 0.0303030303 + 1.515510216 Reorder the terms: 1.515510216 + -2.462121212t + t2 = 0.0303030303 + 1.515510216 Combine like terms: 0.0303030303 + 1.515510216 = 1.5458132463 1.515510216 + -2.462121212t + t2 = 1.5458132463 Factor a perfect square on the left side: (t + -1.231060606)(t + -1.231060606) = 1.5458132463 Calculate the square root of the right side: 1.243307382 Break this problem into two subproblems by setting (t + -1.231060606) equal to 1.243307382 and -1.243307382.Subproblem 1
t + -1.231060606 = 1.243307382 Simplifying t + -1.231060606 = 1.243307382 Reorder the terms: -1.231060606 + t = 1.243307382 Solving -1.231060606 + t = 1.243307382 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.231060606' to each side of the equation. -1.231060606 + 1.231060606 + t = 1.243307382 + 1.231060606 Combine like terms: -1.231060606 + 1.231060606 = 0.000000000 0.000000000 + t = 1.243307382 + 1.231060606 t = 1.243307382 + 1.231060606 Combine like terms: 1.243307382 + 1.231060606 = 2.474367988 t = 2.474367988 Simplifying t = 2.474367988Subproblem 2
t + -1.231060606 = -1.243307382 Simplifying t + -1.231060606 = -1.243307382 Reorder the terms: -1.231060606 + t = -1.243307382 Solving -1.231060606 + t = -1.243307382 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.231060606' to each side of the equation. -1.231060606 + 1.231060606 + t = -1.243307382 + 1.231060606 Combine like terms: -1.231060606 + 1.231060606 = 0.000000000 0.000000000 + t = -1.243307382 + 1.231060606 t = -1.243307382 + 1.231060606 Combine like terms: -1.243307382 + 1.231060606 = -0.012246776 t = -0.012246776 Simplifying t = -0.012246776Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.474367988, -0.012246776}
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