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Simplifying 4 + 25.5t + -4.9t2 = 0 Solving 4 + 25.5t + -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'. -0.8163265306 + -5.204081633t + t2 = 0 Move the constant term to the right: Add '0.8163265306' to each side of the equation. -0.8163265306 + -5.204081633t + 0.8163265306 + t2 = 0 + 0.8163265306 Reorder the terms: -0.8163265306 + 0.8163265306 + -5.204081633t + t2 = 0 + 0.8163265306 Combine like terms: -0.8163265306 + 0.8163265306 = 0.0000000000 0.0000000000 + -5.204081633t + t2 = 0 + 0.8163265306 -5.204081633t + t2 = 0 + 0.8163265306 Combine like terms: 0 + 0.8163265306 = 0.8163265306 -5.204081633t + t2 = 0.8163265306 The t term is -5.204081633t. Take half its coefficient (-2.602040817). Square it (6.770616413) and add it to both sides. Add '6.770616413' to each side of the equation. -5.204081633t + 6.770616413 + t2 = 0.8163265306 + 6.770616413 Reorder the terms: 6.770616413 + -5.204081633t + t2 = 0.8163265306 + 6.770616413 Combine like terms: 0.8163265306 + 6.770616413 = 7.5869429436 6.770616413 + -5.204081633t + t2 = 7.5869429436 Factor a perfect square on the left side: (t + -2.602040817)(t + -2.602040817) = 7.5869429436 Calculate the square root of the right side: 2.754440586 Break this problem into two subproblems by setting (t + -2.602040817) equal to 2.754440586 and -2.754440586.Subproblem 1
t + -2.602040817 = 2.754440586 Simplifying t + -2.602040817 = 2.754440586 Reorder the terms: -2.602040817 + t = 2.754440586 Solving -2.602040817 + t = 2.754440586 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.602040817' to each side of the equation. -2.602040817 + 2.602040817 + t = 2.754440586 + 2.602040817 Combine like terms: -2.602040817 + 2.602040817 = 0.000000000 0.000000000 + t = 2.754440586 + 2.602040817 t = 2.754440586 + 2.602040817 Combine like terms: 2.754440586 + 2.602040817 = 5.356481403 t = 5.356481403 Simplifying t = 5.356481403Subproblem 2
t + -2.602040817 = -2.754440586 Simplifying t + -2.602040817 = -2.754440586 Reorder the terms: -2.602040817 + t = -2.754440586 Solving -2.602040817 + t = -2.754440586 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.602040817' to each side of the equation. -2.602040817 + 2.602040817 + t = -2.754440586 + 2.602040817 Combine like terms: -2.602040817 + 2.602040817 = 0.000000000 0.000000000 + t = -2.754440586 + 2.602040817 t = -2.754440586 + 2.602040817 Combine like terms: -2.754440586 + 2.602040817 = -0.152399769 t = -0.152399769 Simplifying t = -0.152399769Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.356481403, -0.152399769}
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