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Simplifying 3t2 + -38.89t = 77.78 Reorder the terms: -38.89t + 3t2 = 77.78 Solving -38.89t + 3t2 = 77.78 Solving for variable 't'. Reorder the terms: -77.78 + -38.89t + 3t2 = 77.78 + -77.78 Combine like terms: 77.78 + -77.78 = 0.00 -77.78 + -38.89t + 3t2 = 0.00 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -25.92666667 + -12.96333333t + t2 = 0.00 Move the constant term to the right: Add '25.92666667' to each side of the equation. -25.92666667 + -12.96333333t + 25.92666667 + t2 = 0.00 + 25.92666667 Reorder the terms: -25.92666667 + 25.92666667 + -12.96333333t + t2 = 0.00 + 25.92666667 Combine like terms: -25.92666667 + 25.92666667 = 0.00000000 0.00000000 + -12.96333333t + t2 = 0.00 + 25.92666667 -12.96333333t + t2 = 0.00 + 25.92666667 Combine like terms: 0.00 + 25.92666667 = 25.92666667 -12.96333333t + t2 = 25.92666667 The t term is -12.96333333t. Take half its coefficient (-6.481666665). Square it (42.01200276) and add it to both sides. Add '42.01200276' to each side of the equation. -12.96333333t + 42.01200276 + t2 = 25.92666667 + 42.01200276 Reorder the terms: 42.01200276 + -12.96333333t + t2 = 25.92666667 + 42.01200276 Combine like terms: 25.92666667 + 42.01200276 = 67.93866943 42.01200276 + -12.96333333t + t2 = 67.93866943 Factor a perfect square on the left side: (t + -6.481666665)(t + -6.481666665) = 67.93866943 Calculate the square root of the right side: 8.2424917 Break this problem into two subproblems by setting (t + -6.481666665) equal to 8.2424917 and -8.2424917.Subproblem 1
t + -6.481666665 = 8.2424917 Simplifying t + -6.481666665 = 8.2424917 Reorder the terms: -6.481666665 + t = 8.2424917 Solving -6.481666665 + t = 8.2424917 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.481666665' to each side of the equation. -6.481666665 + 6.481666665 + t = 8.2424917 + 6.481666665 Combine like terms: -6.481666665 + 6.481666665 = 0.000000000 0.000000000 + t = 8.2424917 + 6.481666665 t = 8.2424917 + 6.481666665 Combine like terms: 8.2424917 + 6.481666665 = 14.724158365 t = 14.724158365 Simplifying t = 14.724158365Subproblem 2
t + -6.481666665 = -8.2424917 Simplifying t + -6.481666665 = -8.2424917 Reorder the terms: -6.481666665 + t = -8.2424917 Solving -6.481666665 + t = -8.2424917 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.481666665' to each side of the equation. -6.481666665 + 6.481666665 + t = -8.2424917 + 6.481666665 Combine like terms: -6.481666665 + 6.481666665 = 0.000000000 0.000000000 + t = -8.2424917 + 6.481666665 t = -8.2424917 + 6.481666665 Combine like terms: -8.2424917 + 6.481666665 = -1.760825035 t = -1.760825035 Simplifying t = -1.760825035Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.724158365, -1.760825035}
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