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Simplifying -4.9t2 + 8t + 63 = 0 Reorder the terms: 63 + 8t + -4.9t2 = 0 Solving 63 + 8t + -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'. -12.85714286 + -1.632653061t + t2 = 0 Move the constant term to the right: Add '12.85714286' to each side of the equation. -12.85714286 + -1.632653061t + 12.85714286 + t2 = 0 + 12.85714286 Reorder the terms: -12.85714286 + 12.85714286 + -1.632653061t + t2 = 0 + 12.85714286 Combine like terms: -12.85714286 + 12.85714286 = 0.00000000 0.00000000 + -1.632653061t + t2 = 0 + 12.85714286 -1.632653061t + t2 = 0 + 12.85714286 Combine like terms: 0 + 12.85714286 = 12.85714286 -1.632653061t + t2 = 12.85714286 The t term is -1.632653061t. Take half its coefficient (-0.8163265305). Square it (0.6663890044) and add it to both sides. Add '0.6663890044' to each side of the equation. -1.632653061t + 0.6663890044 + t2 = 12.85714286 + 0.6663890044 Reorder the terms: 0.6663890044 + -1.632653061t + t2 = 12.85714286 + 0.6663890044 Combine like terms: 12.85714286 + 0.6663890044 = 13.5235318644 0.6663890044 + -1.632653061t + t2 = 13.5235318644 Factor a perfect square on the left side: (t + -0.8163265305)(t + -0.8163265305) = 13.5235318644 Calculate the square root of the right side: 3.677435501 Break this problem into two subproblems by setting (t + -0.8163265305) equal to 3.677435501 and -3.677435501.Subproblem 1
t + -0.8163265305 = 3.677435501 Simplifying t + -0.8163265305 = 3.677435501 Reorder the terms: -0.8163265305 + t = 3.677435501 Solving -0.8163265305 + t = 3.677435501 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8163265305' to each side of the equation. -0.8163265305 + 0.8163265305 + t = 3.677435501 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + t = 3.677435501 + 0.8163265305 t = 3.677435501 + 0.8163265305 Combine like terms: 3.677435501 + 0.8163265305 = 4.4937620315 t = 4.4937620315 Simplifying t = 4.4937620315Subproblem 2
t + -0.8163265305 = -3.677435501 Simplifying t + -0.8163265305 = -3.677435501 Reorder the terms: -0.8163265305 + t = -3.677435501 Solving -0.8163265305 + t = -3.677435501 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8163265305' to each side of the equation. -0.8163265305 + 0.8163265305 + t = -3.677435501 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + t = -3.677435501 + 0.8163265305 t = -3.677435501 + 0.8163265305 Combine like terms: -3.677435501 + 0.8163265305 = -2.8611089705 t = -2.8611089705 Simplifying t = -2.8611089705Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.4937620315, -2.8611089705}
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