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Simplifying -4.9t2 + 540t + 25 = 750 Reorder the terms: 25 + 540t + -4.9t2 = 750 Solving 25 + 540t + -4.9t2 = 750 Solving for variable 't'. Reorder the terms: 25 + -750 + 540t + -4.9t2 = 750 + -750 Combine like terms: 25 + -750 = -725 -725 + 540t + -4.9t2 = 750 + -750 Combine like terms: 750 + -750 = 0 -725 + 540t + -4.9t2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 147.9591837 + -110.2040816t + t2 = 0 Move the constant term to the right: Add '-147.9591837' to each side of the equation. 147.9591837 + -110.2040816t + -147.9591837 + t2 = 0 + -147.9591837 Reorder the terms: 147.9591837 + -147.9591837 + -110.2040816t + t2 = 0 + -147.9591837 Combine like terms: 147.9591837 + -147.9591837 = 0.0000000 0.0000000 + -110.2040816t + t2 = 0 + -147.9591837 -110.2040816t + t2 = 0 + -147.9591837 Combine like terms: 0 + -147.9591837 = -147.9591837 -110.2040816t + t2 = -147.9591837 The t term is -110.2040816t. Take half its coefficient (-55.1020408). Square it (3036.234900) and add it to both sides. Add '3036.234900' to each side of the equation. -110.2040816t + 3036.234900 + t2 = -147.9591837 + 3036.234900 Reorder the terms: 3036.234900 + -110.2040816t + t2 = -147.9591837 + 3036.234900 Combine like terms: -147.9591837 + 3036.234900 = 2888.2757163 3036.234900 + -110.2040816t + t2 = 2888.2757163 Factor a perfect square on the left side: (t + -55.1020408)(t + -55.1020408) = 2888.2757163 Calculate the square root of the right side: 53.742680583 Break this problem into two subproblems by setting (t + -55.1020408) equal to 53.742680583 and -53.742680583.Subproblem 1
t + -55.1020408 = 53.742680583 Simplifying t + -55.1020408 = 53.742680583 Reorder the terms: -55.1020408 + t = 53.742680583 Solving -55.1020408 + t = 53.742680583 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '55.1020408' to each side of the equation. -55.1020408 + 55.1020408 + t = 53.742680583 + 55.1020408 Combine like terms: -55.1020408 + 55.1020408 = 0.0000000 0.0000000 + t = 53.742680583 + 55.1020408 t = 53.742680583 + 55.1020408 Combine like terms: 53.742680583 + 55.1020408 = 108.844721383 t = 108.844721383 Simplifying t = 108.844721383Subproblem 2
t + -55.1020408 = -53.742680583 Simplifying t + -55.1020408 = -53.742680583 Reorder the terms: -55.1020408 + t = -53.742680583 Solving -55.1020408 + t = -53.742680583 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '55.1020408' to each side of the equation. -55.1020408 + 55.1020408 + t = -53.742680583 + 55.1020408 Combine like terms: -55.1020408 + 55.1020408 = 0.0000000 0.0000000 + t = -53.742680583 + 55.1020408 t = -53.742680583 + 55.1020408 Combine like terms: -53.742680583 + 55.1020408 = 1.359360217 t = 1.359360217 Simplifying t = 1.359360217Solution
The solution to the problem is based on the solutions from the subproblems. t = {108.844721383, 1.359360217}
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