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Simplifying 0 = -4.9t2 + 11t + 400 Reorder the terms: 0 = 400 + 11t + -4.9t2 Solving 0 = 400 + 11t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -400 = -400 -400 + -11t + 4.9t2 = 400 + 11t + -4.9t2 + -400 + -11t + 4.9t2 Reorder the terms: -400 + -11t + 4.9t2 = 400 + -400 + 11t + -11t + -4.9t2 + 4.9t2 Combine like terms: 400 + -400 = 0 -400 + -11t + 4.9t2 = 0 + 11t + -11t + -4.9t2 + 4.9t2 -400 + -11t + 4.9t2 = 11t + -11t + -4.9t2 + 4.9t2 Combine like terms: 11t + -11t = 0 -400 + -11t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -400 + -11t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -400 + -11t + 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'. -81.63265306 + -2.244897959t + t2 = 0 Move the constant term to the right: Add '81.63265306' to each side of the equation. -81.63265306 + -2.244897959t + 81.63265306 + t2 = 0 + 81.63265306 Reorder the terms: -81.63265306 + 81.63265306 + -2.244897959t + t2 = 0 + 81.63265306 Combine like terms: -81.63265306 + 81.63265306 = 0.00000000 0.00000000 + -2.244897959t + t2 = 0 + 81.63265306 -2.244897959t + t2 = 0 + 81.63265306 Combine like terms: 0 + 81.63265306 = 81.63265306 -2.244897959t + t2 = 81.63265306 The t term is -2.244897959t. Take half its coefficient (-1.12244898). Square it (1.259891713) and add it to both sides. Add '1.259891713' to each side of the equation. -2.244897959t + 1.259891713 + t2 = 81.63265306 + 1.259891713 Reorder the terms: 1.259891713 + -2.244897959t + t2 = 81.63265306 + 1.259891713 Combine like terms: 81.63265306 + 1.259891713 = 82.892544773 1.259891713 + -2.244897959t + t2 = 82.892544773 Factor a perfect square on the left side: (t + -1.12244898)(t + -1.12244898) = 82.892544773 Calculate the square root of the right side: 9.104534297 Break this problem into two subproblems by setting (t + -1.12244898) equal to 9.104534297 and -9.104534297.Subproblem 1
t + -1.12244898 = 9.104534297 Simplifying t + -1.12244898 = 9.104534297 Reorder the terms: -1.12244898 + t = 9.104534297 Solving -1.12244898 + t = 9.104534297 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + t = 9.104534297 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = 9.104534297 + 1.12244898 t = 9.104534297 + 1.12244898 Combine like terms: 9.104534297 + 1.12244898 = 10.226983277 t = 10.226983277 Simplifying t = 10.226983277Subproblem 2
t + -1.12244898 = -9.104534297 Simplifying t + -1.12244898 = -9.104534297 Reorder the terms: -1.12244898 + t = -9.104534297 Solving -1.12244898 + t = -9.104534297 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + t = -9.104534297 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = -9.104534297 + 1.12244898 t = -9.104534297 + 1.12244898 Combine like terms: -9.104534297 + 1.12244898 = -7.982085317 t = -7.982085317 Simplifying t = -7.982085317Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.226983277, -7.982085317}
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