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Simplifying -0.921 = -2.04t + 0.5 * -9.8t2 Multiply 0.5 * -9.8 -0.921 = -2.04t + -4.9t2 Solving -0.921 = -2.04t + -4.9t2 Solving for variable 't'. Reorder the terms: -0.921 + 2.04t + 4.9t2 = -2.04t + 2.04t + -4.9t2 + 4.9t2 Combine like terms: -2.04t + 2.04t = 0.00 -0.921 + 2.04t + 4.9t2 = 0.00 + -4.9t2 + 4.9t2 -0.921 + 2.04t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -0.921 + 2.04t + 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'. -0.1879591837 + 0.4163265306t + t2 = 0 Move the constant term to the right: Add '0.1879591837' to each side of the equation. -0.1879591837 + 0.4163265306t + 0.1879591837 + t2 = 0 + 0.1879591837 Reorder the terms: -0.1879591837 + 0.1879591837 + 0.4163265306t + t2 = 0 + 0.1879591837 Combine like terms: -0.1879591837 + 0.1879591837 = 0.0000000000 0.0000000000 + 0.4163265306t + t2 = 0 + 0.1879591837 0.4163265306t + t2 = 0 + 0.1879591837 Combine like terms: 0 + 0.1879591837 = 0.1879591837 0.4163265306t + t2 = 0.1879591837 The t term is 0.4163265306t. Take half its coefficient (0.2081632653). Square it (0.04333194502) and add it to both sides. Add '0.04333194502' to each side of the equation. 0.4163265306t + 0.04333194502 + t2 = 0.1879591837 + 0.04333194502 Reorder the terms: 0.04333194502 + 0.4163265306t + t2 = 0.1879591837 + 0.04333194502 Combine like terms: 0.1879591837 + 0.04333194502 = 0.23129112872 0.04333194502 + 0.4163265306t + t2 = 0.23129112872 Factor a perfect square on the left side: (t + 0.2081632653)(t + 0.2081632653) = 0.23129112872 Calculate the square root of the right side: 0.480927363 Break this problem into two subproblems by setting (t + 0.2081632653) equal to 0.480927363 and -0.480927363.Subproblem 1
t + 0.2081632653 = 0.480927363 Simplifying t + 0.2081632653 = 0.480927363 Reorder the terms: 0.2081632653 + t = 0.480927363 Solving 0.2081632653 + t = 0.480927363 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2081632653' to each side of the equation. 0.2081632653 + -0.2081632653 + t = 0.480927363 + -0.2081632653 Combine like terms: 0.2081632653 + -0.2081632653 = 0.0000000000 0.0000000000 + t = 0.480927363 + -0.2081632653 t = 0.480927363 + -0.2081632653 Combine like terms: 0.480927363 + -0.2081632653 = 0.2727640977 t = 0.2727640977 Simplifying t = 0.2727640977Subproblem 2
t + 0.2081632653 = -0.480927363 Simplifying t + 0.2081632653 = -0.480927363 Reorder the terms: 0.2081632653 + t = -0.480927363 Solving 0.2081632653 + t = -0.480927363 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2081632653' to each side of the equation. 0.2081632653 + -0.2081632653 + t = -0.480927363 + -0.2081632653 Combine like terms: 0.2081632653 + -0.2081632653 = 0.0000000000 0.0000000000 + t = -0.480927363 + -0.2081632653 t = -0.480927363 + -0.2081632653 Combine like terms: -0.480927363 + -0.2081632653 = -0.6890906283 t = -0.6890906283 Simplifying t = -0.6890906283Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.2727640977, -0.6890906283}
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