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Simplifying 4 = 13t + 0.5 * 9.8t2 Multiply 0.5 * 9.8 4 = 13t + 4.9t2 Solving 4 = 13t + 4.9t2 Solving for variable 't'. Reorder the terms: 4 + -13t + -4.9t2 = 13t + -13t + 4.9t2 + -4.9t2 Combine like terms: 13t + -13t = 0 4 + -13t + -4.9t2 = 0 + 4.9t2 + -4.9t2 4 + -13t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 4 + -13t + -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'. -0.8163265306 + 2.653061224t + t2 = 0 Move the constant term to the right: Add '0.8163265306' to each side of the equation. -0.8163265306 + 2.653061224t + 0.8163265306 + t2 = 0 + 0.8163265306 Reorder the terms: -0.8163265306 + 0.8163265306 + 2.653061224t + t2 = 0 + 0.8163265306 Combine like terms: -0.8163265306 + 0.8163265306 = 0.0000000000 0.0000000000 + 2.653061224t + t2 = 0 + 0.8163265306 2.653061224t + t2 = 0 + 0.8163265306 Combine like terms: 0 + 0.8163265306 = 0.8163265306 2.653061224t + t2 = 0.8163265306 The t term is 2.653061224t. Take half its coefficient (1.326530612). Square it (1.759683465) and add it to both sides. Add '1.759683465' to each side of the equation. 2.653061224t + 1.759683465 + t2 = 0.8163265306 + 1.759683465 Reorder the terms: 1.759683465 + 2.653061224t + t2 = 0.8163265306 + 1.759683465 Combine like terms: 0.8163265306 + 1.759683465 = 2.5760099956 1.759683465 + 2.653061224t + t2 = 2.5760099956 Factor a perfect square on the left side: (t + 1.326530612)(t + 1.326530612) = 2.5760099956 Calculate the square root of the right side: 1.604995326 Break this problem into two subproblems by setting (t + 1.326530612) equal to 1.604995326 and -1.604995326.Subproblem 1
t + 1.326530612 = 1.604995326 Simplifying t + 1.326530612 = 1.604995326 Reorder the terms: 1.326530612 + t = 1.604995326 Solving 1.326530612 + t = 1.604995326 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.326530612' to each side of the equation. 1.326530612 + -1.326530612 + t = 1.604995326 + -1.326530612 Combine like terms: 1.326530612 + -1.326530612 = 0.000000000 0.000000000 + t = 1.604995326 + -1.326530612 t = 1.604995326 + -1.326530612 Combine like terms: 1.604995326 + -1.326530612 = 0.278464714 t = 0.278464714 Simplifying t = 0.278464714Subproblem 2
t + 1.326530612 = -1.604995326 Simplifying t + 1.326530612 = -1.604995326 Reorder the terms: 1.326530612 + t = -1.604995326 Solving 1.326530612 + t = -1.604995326 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.326530612' to each side of the equation. 1.326530612 + -1.326530612 + t = -1.604995326 + -1.326530612 Combine like terms: 1.326530612 + -1.326530612 = 0.000000000 0.000000000 + t = -1.604995326 + -1.326530612 t = -1.604995326 + -1.326530612 Combine like terms: -1.604995326 + -1.326530612 = -2.931525938 t = -2.931525938 Simplifying t = -2.931525938Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.278464714, -2.931525938}
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