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Simplifying 0 = -4.9t2 + 28t + 90 Reorder the terms: 0 = 90 + 28t + -4.9t2 Solving 0 = 90 + 28t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -90 = -90 -90 + -28t + 4.9t2 = 90 + 28t + -4.9t2 + -90 + -28t + 4.9t2 Reorder the terms: -90 + -28t + 4.9t2 = 90 + -90 + 28t + -28t + -4.9t2 + 4.9t2 Combine like terms: 90 + -90 = 0 -90 + -28t + 4.9t2 = 0 + 28t + -28t + -4.9t2 + 4.9t2 -90 + -28t + 4.9t2 = 28t + -28t + -4.9t2 + 4.9t2 Combine like terms: 28t + -28t = 0 -90 + -28t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -90 + -28t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -90 + -28t + 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'. -18.36734694 + -5.714285714t + t2 = 0 Move the constant term to the right: Add '18.36734694' to each side of the equation. -18.36734694 + -5.714285714t + 18.36734694 + t2 = 0 + 18.36734694 Reorder the terms: -18.36734694 + 18.36734694 + -5.714285714t + t2 = 0 + 18.36734694 Combine like terms: -18.36734694 + 18.36734694 = 0.00000000 0.00000000 + -5.714285714t + t2 = 0 + 18.36734694 -5.714285714t + t2 = 0 + 18.36734694 Combine like terms: 0 + 18.36734694 = 18.36734694 -5.714285714t + t2 = 18.36734694 The t term is -5.714285714t. Take half its coefficient (-2.857142857). Square it (8.163265305) and add it to both sides. Add '8.163265305' to each side of the equation. -5.714285714t + 8.163265305 + t2 = 18.36734694 + 8.163265305 Reorder the terms: 8.163265305 + -5.714285714t + t2 = 18.36734694 + 8.163265305 Combine like terms: 18.36734694 + 8.163265305 = 26.530612245 8.163265305 + -5.714285714t + t2 = 26.530612245 Factor a perfect square on the left side: (t + -2.857142857)(t + -2.857142857) = 26.530612245 Calculate the square root of the right side: 5.150787536 Break this problem into two subproblems by setting (t + -2.857142857) equal to 5.150787536 and -5.150787536.Subproblem 1
t + -2.857142857 = 5.150787536 Simplifying t + -2.857142857 = 5.150787536 Reorder the terms: -2.857142857 + t = 5.150787536 Solving -2.857142857 + t = 5.150787536 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.857142857' to each side of the equation. -2.857142857 + 2.857142857 + t = 5.150787536 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + t = 5.150787536 + 2.857142857 t = 5.150787536 + 2.857142857 Combine like terms: 5.150787536 + 2.857142857 = 8.007930393 t = 8.007930393 Simplifying t = 8.007930393Subproblem 2
t + -2.857142857 = -5.150787536 Simplifying t + -2.857142857 = -5.150787536 Reorder the terms: -2.857142857 + t = -5.150787536 Solving -2.857142857 + t = -5.150787536 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.857142857' to each side of the equation. -2.857142857 + 2.857142857 + t = -5.150787536 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + t = -5.150787536 + 2.857142857 t = -5.150787536 + 2.857142857 Combine like terms: -5.150787536 + 2.857142857 = -2.293644679 t = -2.293644679 Simplifying t = -2.293644679Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.007930393, -2.293644679}
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