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Simplifying 10(t) = -4.9t2 + 3.5t + 10 Reorder the terms: 10t = 10 + 3.5t + -4.9t2 Solving 10t = 10 + 3.5t + -4.9t2 Solving for variable 't'. Reorder the terms: -10 + 10t + -3.5t + 4.9t2 = 10 + 3.5t + -4.9t2 + -10 + -3.5t + 4.9t2 Combine like terms: 10t + -3.5t = 6.5t -10 + 6.5t + 4.9t2 = 10 + 3.5t + -4.9t2 + -10 + -3.5t + 4.9t2 Reorder the terms: -10 + 6.5t + 4.9t2 = 10 + -10 + 3.5t + -3.5t + -4.9t2 + 4.9t2 Combine like terms: 10 + -10 = 0 -10 + 6.5t + 4.9t2 = 0 + 3.5t + -3.5t + -4.9t2 + 4.9t2 -10 + 6.5t + 4.9t2 = 3.5t + -3.5t + -4.9t2 + 4.9t2 Combine like terms: 3.5t + -3.5t = 0.0 -10 + 6.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -10 + 6.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -10 + 6.5t + 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'. -2.040816327 + 1.326530612t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + 1.326530612t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + 1.326530612t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + 1.326530612t + t2 = 0 + 2.040816327 1.326530612t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 1.326530612t + t2 = 2.040816327 The t term is 1.326530612t. Take half its coefficient (0.663265306). Square it (0.4399208661) and add it to both sides. Add '0.4399208661' to each side of the equation. 1.326530612t + 0.4399208661 + t2 = 2.040816327 + 0.4399208661 Reorder the terms: 0.4399208661 + 1.326530612t + t2 = 2.040816327 + 0.4399208661 Combine like terms: 2.040816327 + 0.4399208661 = 2.4807371931 0.4399208661 + 1.326530612t + t2 = 2.4807371931 Factor a perfect square on the left side: (t + 0.663265306)(t + 0.663265306) = 2.4807371931 Calculate the square root of the right side: 1.575035616 Break this problem into two subproblems by setting (t + 0.663265306) equal to 1.575035616 and -1.575035616.Subproblem 1
t + 0.663265306 = 1.575035616 Simplifying t + 0.663265306 = 1.575035616 Reorder the terms: 0.663265306 + t = 1.575035616 Solving 0.663265306 + t = 1.575035616 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.663265306' to each side of the equation. 0.663265306 + -0.663265306 + t = 1.575035616 + -0.663265306 Combine like terms: 0.663265306 + -0.663265306 = 0.000000000 0.000000000 + t = 1.575035616 + -0.663265306 t = 1.575035616 + -0.663265306 Combine like terms: 1.575035616 + -0.663265306 = 0.91177031 t = 0.91177031 Simplifying t = 0.91177031Subproblem 2
t + 0.663265306 = -1.575035616 Simplifying t + 0.663265306 = -1.575035616 Reorder the terms: 0.663265306 + t = -1.575035616 Solving 0.663265306 + t = -1.575035616 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.663265306' to each side of the equation. 0.663265306 + -0.663265306 + t = -1.575035616 + -0.663265306 Combine like terms: 0.663265306 + -0.663265306 = 0.000000000 0.000000000 + t = -1.575035616 + -0.663265306 t = -1.575035616 + -0.663265306 Combine like terms: -1.575035616 + -0.663265306 = -2.238300922 t = -2.238300922 Simplifying t = -2.238300922Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.91177031, -2.238300922}
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