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Simplifying 4.9t2 + -25t + 10 = 0 Reorder the terms: 10 + -25t + 4.9t2 = 0 Solving 10 + -25t + 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'. 2.040816327 + -5.102040816t + t2 = 0 Move the constant term to the right: Add '-2.040816327' to each side of the equation. 2.040816327 + -5.102040816t + -2.040816327 + t2 = 0 + -2.040816327 Reorder the terms: 2.040816327 + -2.040816327 + -5.102040816t + t2 = 0 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + -5.102040816t + t2 = 0 + -2.040816327 -5.102040816t + t2 = 0 + -2.040816327 Combine like terms: 0 + -2.040816327 = -2.040816327 -5.102040816t + t2 = -2.040816327 The t term is -5.102040816t. Take half its coefficient (-2.551020408). Square it (6.507705122) and add it to both sides. Add '6.507705122' to each side of the equation. -5.102040816t + 6.507705122 + t2 = -2.040816327 + 6.507705122 Reorder the terms: 6.507705122 + -5.102040816t + t2 = -2.040816327 + 6.507705122 Combine like terms: -2.040816327 + 6.507705122 = 4.466888795 6.507705122 + -5.102040816t + t2 = 4.466888795 Factor a perfect square on the left side: (t + -2.551020408)(t + -2.551020408) = 4.466888795 Calculate the square root of the right side: 2.113501548 Break this problem into two subproblems by setting (t + -2.551020408) equal to 2.113501548 and -2.113501548.Subproblem 1
t + -2.551020408 = 2.113501548 Simplifying t + -2.551020408 = 2.113501548 Reorder the terms: -2.551020408 + t = 2.113501548 Solving -2.551020408 + t = 2.113501548 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.551020408' to each side of the equation. -2.551020408 + 2.551020408 + t = 2.113501548 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = 2.113501548 + 2.551020408 t = 2.113501548 + 2.551020408 Combine like terms: 2.113501548 + 2.551020408 = 4.664521956 t = 4.664521956 Simplifying t = 4.664521956Subproblem 2
t + -2.551020408 = -2.113501548 Simplifying t + -2.551020408 = -2.113501548 Reorder the terms: -2.551020408 + t = -2.113501548 Solving -2.551020408 + t = -2.113501548 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.551020408' to each side of the equation. -2.551020408 + 2.551020408 + t = -2.113501548 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = -2.113501548 + 2.551020408 t = -2.113501548 + 2.551020408 Combine like terms: -2.113501548 + 2.551020408 = 0.43751886 t = 0.43751886 Simplifying t = 0.43751886Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.664521956, 0.43751886}
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