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Simplifying (-4.9t2) + 25t + 2 = 0 Reorder the terms: 2 + 25t + (-4.9t2) = 0 Solving 2 + 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'. -0.4081632653 + -5.102040816t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -5.102040816t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -5.102040816t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -5.102040816t + t2 = 0 + 0.4081632653 -5.102040816t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -5.102040816t + t2 = 0.4081632653 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 = 0.4081632653 + 6.507705122 Reorder the terms: 6.507705122 + -5.102040816t + t2 = 0.4081632653 + 6.507705122 Combine like terms: 0.4081632653 + 6.507705122 = 6.9158683873 6.507705122 + -5.102040816t + t2 = 6.9158683873 Factor a perfect square on the left side: ((t) + -2.551020408)((t) + -2.551020408) = 6.9158683873 Calculate the square root of the right side: 2.629803869 Break this problem into two subproblems by setting ((t) + -2.551020408) equal to 2.629803869 and -2.629803869.Subproblem 1
(t) + -2.551020408 = 2.629803869 Simplifying (t) + -2.551020408 = 2.629803869 t + -2.551020408 = 2.629803869 Reorder the terms: -2.551020408 + t = 2.629803869 Solving -2.551020408 + t = 2.629803869 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 = 2.629803869 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = 2.629803869 + 2.551020408 t = 2.629803869 + 2.551020408 Combine like terms: 2.629803869 + 2.551020408 = 5.180824277 t = 5.180824277 Simplifying t = 5.180824277Subproblem 2
(t) + -2.551020408 = -2.629803869 Simplifying (t) + -2.551020408 = -2.629803869 t + -2.551020408 = -2.629803869 Reorder the terms: -2.551020408 + t = -2.629803869 Solving -2.551020408 + t = -2.629803869 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 = -2.629803869 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = -2.629803869 + 2.551020408 t = -2.629803869 + 2.551020408 Combine like terms: -2.629803869 + 2.551020408 = -0.078783461 t = -0.078783461 Simplifying t = -0.078783461Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.180824277, -0.078783461}
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