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Simplifying -4.9t2 + 30t + 16 = 0 Reorder the terms: 16 + 30t + -4.9t2 = 0 Solving 16 + 30t + -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'. -3.265306122 + -6.12244898t + t2 = 0 Move the constant term to the right: Add '3.265306122' to each side of the equation. -3.265306122 + -6.12244898t + 3.265306122 + t2 = 0 + 3.265306122 Reorder the terms: -3.265306122 + 3.265306122 + -6.12244898t + t2 = 0 + 3.265306122 Combine like terms: -3.265306122 + 3.265306122 = 0.000000000 0.000000000 + -6.12244898t + t2 = 0 + 3.265306122 -6.12244898t + t2 = 0 + 3.265306122 Combine like terms: 0 + 3.265306122 = 3.265306122 -6.12244898t + t2 = 3.265306122 The t term is -6.12244898t. Take half its coefficient (-3.06122449). Square it (9.371095378) and add it to both sides. Add '9.371095378' to each side of the equation. -6.12244898t + 9.371095378 + t2 = 3.265306122 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898t + t2 = 3.265306122 + 9.371095378 Combine like terms: 3.265306122 + 9.371095378 = 12.6364015 9.371095378 + -6.12244898t + t2 = 12.6364015 Factor a perfect square on the left side: (t + -3.06122449)(t + -3.06122449) = 12.6364015 Calculate the square root of the right side: 3.554771652 Break this problem into two subproblems by setting (t + -3.06122449) equal to 3.554771652 and -3.554771652.Subproblem 1
t + -3.06122449 = 3.554771652 Simplifying t + -3.06122449 = 3.554771652 Reorder the terms: -3.06122449 + t = 3.554771652 Solving -3.06122449 + t = 3.554771652 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + t = 3.554771652 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = 3.554771652 + 3.06122449 t = 3.554771652 + 3.06122449 Combine like terms: 3.554771652 + 3.06122449 = 6.615996142 t = 6.615996142 Simplifying t = 6.615996142Subproblem 2
t + -3.06122449 = -3.554771652 Simplifying t + -3.06122449 = -3.554771652 Reorder the terms: -3.06122449 + t = -3.554771652 Solving -3.06122449 + t = -3.554771652 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + t = -3.554771652 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = -3.554771652 + 3.06122449 t = -3.554771652 + 3.06122449 Combine like terms: -3.554771652 + 3.06122449 = -0.493547162 t = -0.493547162 Simplifying t = -0.493547162Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.615996142, -0.493547162}
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