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Simplifying -4.9t2 + 2.5t + 1 = 0 Reorder the terms: 1 + 2.5t + -4.9t2 = 0 Solving 1 + 2.5t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.2040816327 + -0.5102040816t + t2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -0.5102040816t + 0.2040816327 + t2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -0.5102040816t + t2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -0.5102040816t + t2 = 0 + 0.2040816327 -0.5102040816t + t2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -0.5102040816t + t2 = 0.2040816327 The t term is -0.5102040816t. Take half its coefficient (-0.2551020408). Square it (0.06507705122) and add it to both sides. Add '0.06507705122' to each side of the equation. -0.5102040816t + 0.06507705122 + t2 = 0.2040816327 + 0.06507705122 Reorder the terms: 0.06507705122 + -0.5102040816t + t2 = 0.2040816327 + 0.06507705122 Combine like terms: 0.2040816327 + 0.06507705122 = 0.26915868392 0.06507705122 + -0.5102040816t + t2 = 0.26915868392 Factor a perfect square on the left side: (t + -0.2551020408)(t + -0.2551020408) = 0.26915868392 Calculate the square root of the right side: 0.518805054 Break this problem into two subproblems by setting (t + -0.2551020408) equal to 0.518805054 and -0.518805054.Subproblem 1
t + -0.2551020408 = 0.518805054 Simplifying t + -0.2551020408 = 0.518805054 Reorder the terms: -0.2551020408 + t = 0.518805054 Solving -0.2551020408 + t = 0.518805054 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2551020408' to each side of the equation. -0.2551020408 + 0.2551020408 + t = 0.518805054 + 0.2551020408 Combine like terms: -0.2551020408 + 0.2551020408 = 0.0000000000 0.0000000000 + t = 0.518805054 + 0.2551020408 t = 0.518805054 + 0.2551020408 Combine like terms: 0.518805054 + 0.2551020408 = 0.7739070948 t = 0.7739070948 Simplifying t = 0.7739070948Subproblem 2
t + -0.2551020408 = -0.518805054 Simplifying t + -0.2551020408 = -0.518805054 Reorder the terms: -0.2551020408 + t = -0.518805054 Solving -0.2551020408 + t = -0.518805054 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2551020408' to each side of the equation. -0.2551020408 + 0.2551020408 + t = -0.518805054 + 0.2551020408 Combine like terms: -0.2551020408 + 0.2551020408 = 0.0000000000 0.0000000000 + t = -0.518805054 + 0.2551020408 t = -0.518805054 + 0.2551020408 Combine like terms: -0.518805054 + 0.2551020408 = -0.2637030132 t = -0.2637030132 Simplifying t = -0.2637030132Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.7739070948, -0.2637030132}
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