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Simplifying 20 = 25t + -4.9t2 Solving 20 = 25t + -4.9t2 Solving for variable 't'. Reorder the terms: 20 + -25t + 4.9t2 = 25t + -25t + -4.9t2 + 4.9t2 Combine like terms: 25t + -25t = 0 20 + -25t + 4.9t2 = 0 + -4.9t2 + 4.9t2 20 + -25t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 20 + -25t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 4.081632653 + -5.102040816t + t2 = 0 Move the constant term to the right: Add '-4.081632653' to each side of the equation. 4.081632653 + -5.102040816t + -4.081632653 + t2 = 0 + -4.081632653 Reorder the terms: 4.081632653 + -4.081632653 + -5.102040816t + t2 = 0 + -4.081632653 Combine like terms: 4.081632653 + -4.081632653 = 0.000000000 0.000000000 + -5.102040816t + t2 = 0 + -4.081632653 -5.102040816t + t2 = 0 + -4.081632653 Combine like terms: 0 + -4.081632653 = -4.081632653 -5.102040816t + t2 = -4.081632653 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 = -4.081632653 + 6.507705122 Reorder the terms: 6.507705122 + -5.102040816t + t2 = -4.081632653 + 6.507705122 Combine like terms: -4.081632653 + 6.507705122 = 2.426072469 6.507705122 + -5.102040816t + t2 = 2.426072469 Factor a perfect square on the left side: (t + -2.551020408)(t + -2.551020408) = 2.426072469 Calculate the square root of the right side: 1.557585461 Break this problem into two subproblems by setting (t + -2.551020408) equal to 1.557585461 and -1.557585461.Subproblem 1
t + -2.551020408 = 1.557585461 Simplifying t + -2.551020408 = 1.557585461 Reorder the terms: -2.551020408 + t = 1.557585461 Solving -2.551020408 + t = 1.557585461 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 = 1.557585461 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = 1.557585461 + 2.551020408 t = 1.557585461 + 2.551020408 Combine like terms: 1.557585461 + 2.551020408 = 4.108605869 t = 4.108605869 Simplifying t = 4.108605869Subproblem 2
t + -2.551020408 = -1.557585461 Simplifying t + -2.551020408 = -1.557585461 Reorder the terms: -2.551020408 + t = -1.557585461 Solving -2.551020408 + t = -1.557585461 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 = -1.557585461 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = -1.557585461 + 2.551020408 t = -1.557585461 + 2.551020408 Combine like terms: -1.557585461 + 2.551020408 = 0.993434947 t = 0.993434947 Simplifying t = 0.993434947Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.108605869, 0.993434947}
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