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Simplifying -20.2 = 11.8t + 0.5(-9.8) * t2 Multiply 0.5 * -9.8 -20.2 = 11.8t + -4.9t2 Solving -20.2 = 11.8t + -4.9t2 Solving for variable 't'. Reorder the terms: -20.2 + -11.8t + 4.9t2 = 11.8t + -11.8t + -4.9t2 + 4.9t2 Combine like terms: 11.8t + -11.8t = 0.0 -20.2 + -11.8t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -20.2 + -11.8t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -20.2 + -11.8t + 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'. -4.12244898 + -2.408163265t + t2 = 0 Move the constant term to the right: Add '4.12244898' to each side of the equation. -4.12244898 + -2.408163265t + 4.12244898 + t2 = 0 + 4.12244898 Reorder the terms: -4.12244898 + 4.12244898 + -2.408163265t + t2 = 0 + 4.12244898 Combine like terms: -4.12244898 + 4.12244898 = 0.00000000 0.00000000 + -2.408163265t + t2 = 0 + 4.12244898 -2.408163265t + t2 = 0 + 4.12244898 Combine like terms: 0 + 4.12244898 = 4.12244898 -2.408163265t + t2 = 4.12244898 The t term is -2.408163265t. Take half its coefficient (-1.204081633). Square it (1.449812579) and add it to both sides. Add '1.449812579' to each side of the equation. -2.408163265t + 1.449812579 + t2 = 4.12244898 + 1.449812579 Reorder the terms: 1.449812579 + -2.408163265t + t2 = 4.12244898 + 1.449812579 Combine like terms: 4.12244898 + 1.449812579 = 5.572261559 1.449812579 + -2.408163265t + t2 = 5.572261559 Factor a perfect square on the left side: (t + -1.204081633)(t + -1.204081633) = 5.572261559 Calculate the square root of the right side: 2.360563822 Break this problem into two subproblems by setting (t + -1.204081633) equal to 2.360563822 and -2.360563822.Subproblem 1
t + -1.204081633 = 2.360563822 Simplifying t + -1.204081633 = 2.360563822 Reorder the terms: -1.204081633 + t = 2.360563822 Solving -1.204081633 + t = 2.360563822 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.204081633' to each side of the equation. -1.204081633 + 1.204081633 + t = 2.360563822 + 1.204081633 Combine like terms: -1.204081633 + 1.204081633 = 0.000000000 0.000000000 + t = 2.360563822 + 1.204081633 t = 2.360563822 + 1.204081633 Combine like terms: 2.360563822 + 1.204081633 = 3.564645455 t = 3.564645455 Simplifying t = 3.564645455Subproblem 2
t + -1.204081633 = -2.360563822 Simplifying t + -1.204081633 = -2.360563822 Reorder the terms: -1.204081633 + t = -2.360563822 Solving -1.204081633 + t = -2.360563822 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.204081633' to each side of the equation. -1.204081633 + 1.204081633 + t = -2.360563822 + 1.204081633 Combine like terms: -1.204081633 + 1.204081633 = 0.000000000 0.000000000 + t = -2.360563822 + 1.204081633 t = -2.360563822 + 1.204081633 Combine like terms: -2.360563822 + 1.204081633 = -1.156482189 t = -1.156482189 Simplifying t = -1.156482189Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.564645455, -1.156482189}
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