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Simplifying -4.9t2 + 75t + 40 = 0 Reorder the terms: 40 + 75t + -4.9t2 = 0 Solving 40 + 75t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -8.163265306 + -15.30612245t + t2 = 0 Move the constant term to the right: Add '8.163265306' to each side of the equation. -8.163265306 + -15.30612245t + 8.163265306 + t2 = 0 + 8.163265306 Reorder the terms: -8.163265306 + 8.163265306 + -15.30612245t + t2 = 0 + 8.163265306 Combine like terms: -8.163265306 + 8.163265306 = 0.000000000 0.000000000 + -15.30612245t + t2 = 0 + 8.163265306 -15.30612245t + t2 = 0 + 8.163265306 Combine like terms: 0 + 8.163265306 = 8.163265306 -15.30612245t + t2 = 8.163265306 The t term is -15.30612245t. Take half its coefficient (-7.653061225). Square it (58.56934611) and add it to both sides. Add '58.56934611' to each side of the equation. -15.30612245t + 58.56934611 + t2 = 8.163265306 + 58.56934611 Reorder the terms: 58.56934611 + -15.30612245t + t2 = 8.163265306 + 58.56934611 Combine like terms: 8.163265306 + 58.56934611 = 66.732611416 58.56934611 + -15.30612245t + t2 = 66.732611416 Factor a perfect square on the left side: (t + -7.653061225)(t + -7.653061225) = 66.732611416 Calculate the square root of the right side: 8.169003086 Break this problem into two subproblems by setting (t + -7.653061225) equal to 8.169003086 and -8.169003086.Subproblem 1
t + -7.653061225 = 8.169003086 Simplifying t + -7.653061225 = 8.169003086 Reorder the terms: -7.653061225 + t = 8.169003086 Solving -7.653061225 + t = 8.169003086 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.653061225' to each side of the equation. -7.653061225 + 7.653061225 + t = 8.169003086 + 7.653061225 Combine like terms: -7.653061225 + 7.653061225 = 0.000000000 0.000000000 + t = 8.169003086 + 7.653061225 t = 8.169003086 + 7.653061225 Combine like terms: 8.169003086 + 7.653061225 = 15.822064311 t = 15.822064311 Simplifying t = 15.822064311Subproblem 2
t + -7.653061225 = -8.169003086 Simplifying t + -7.653061225 = -8.169003086 Reorder the terms: -7.653061225 + t = -8.169003086 Solving -7.653061225 + t = -8.169003086 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.653061225' to each side of the equation. -7.653061225 + 7.653061225 + t = -8.169003086 + 7.653061225 Combine like terms: -7.653061225 + 7.653061225 = 0.000000000 0.000000000 + t = -8.169003086 + 7.653061225 t = -8.169003086 + 7.653061225 Combine like terms: -8.169003086 + 7.653061225 = -0.515941861 t = -0.515941861 Simplifying t = -0.515941861Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.822064311, -0.515941861}
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