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Simplifying 0 = -4.9t2 + 6t + 8 Reorder the terms: 0 = 8 + 6t + -4.9t2 Solving 0 = 8 + 6t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -8 = -8 -8 + -6t + 4.9t2 = 8 + 6t + -4.9t2 + -8 + -6t + 4.9t2 Reorder the terms: -8 + -6t + 4.9t2 = 8 + -8 + 6t + -6t + -4.9t2 + 4.9t2 Combine like terms: 8 + -8 = 0 -8 + -6t + 4.9t2 = 0 + 6t + -6t + -4.9t2 + 4.9t2 -8 + -6t + 4.9t2 = 6t + -6t + -4.9t2 + 4.9t2 Combine like terms: 6t + -6t = 0 -8 + -6t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -8 + -6t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -8 + -6t + 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'. -1.632653061 + -1.224489796t + t2 = 0 Move the constant term to the right: Add '1.632653061' to each side of the equation. -1.632653061 + -1.224489796t + 1.632653061 + t2 = 0 + 1.632653061 Reorder the terms: -1.632653061 + 1.632653061 + -1.224489796t + t2 = 0 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + -1.224489796t + t2 = 0 + 1.632653061 -1.224489796t + t2 = 0 + 1.632653061 Combine like terms: 0 + 1.632653061 = 1.632653061 -1.224489796t + t2 = 1.632653061 The t term is -1.224489796t. Take half its coefficient (-0.612244898). Square it (0.3748438151) and add it to both sides. Add '0.3748438151' to each side of the equation. -1.224489796t + 0.3748438151 + t2 = 1.632653061 + 0.3748438151 Reorder the terms: 0.3748438151 + -1.224489796t + t2 = 1.632653061 + 0.3748438151 Combine like terms: 1.632653061 + 0.3748438151 = 2.0074968761 0.3748438151 + -1.224489796t + t2 = 2.0074968761 Factor a perfect square on the left side: (t + -0.612244898)(t + -0.612244898) = 2.0074968761 Calculate the square root of the right side: 1.416861629 Break this problem into two subproblems by setting (t + -0.612244898) equal to 1.416861629 and -1.416861629.Subproblem 1
t + -0.612244898 = 1.416861629 Simplifying t + -0.612244898 = 1.416861629 Reorder the terms: -0.612244898 + t = 1.416861629 Solving -0.612244898 + t = 1.416861629 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.612244898' to each side of the equation. -0.612244898 + 0.612244898 + t = 1.416861629 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + t = 1.416861629 + 0.612244898 t = 1.416861629 + 0.612244898 Combine like terms: 1.416861629 + 0.612244898 = 2.029106527 t = 2.029106527 Simplifying t = 2.029106527Subproblem 2
t + -0.612244898 = -1.416861629 Simplifying t + -0.612244898 = -1.416861629 Reorder the terms: -0.612244898 + t = -1.416861629 Solving -0.612244898 + t = -1.416861629 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.612244898' to each side of the equation. -0.612244898 + 0.612244898 + t = -1.416861629 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + t = -1.416861629 + 0.612244898 t = -1.416861629 + 0.612244898 Combine like terms: -1.416861629 + 0.612244898 = -0.804616731 t = -0.804616731 Simplifying t = -0.804616731Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.029106527, -0.804616731}
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