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Simplifying 9.8t2 + 5.36t + -30 = 0 Reorder the terms: -30 + 5.36t + 9.8t2 = 0 Solving -30 + 5.36t + 9.8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 9.8 the coefficient of the squared term: Divide each side by '9.8'. -3.06122449 + 0.5469387755t + t2 = 0 Move the constant term to the right: Add '3.06122449' to each side of the equation. -3.06122449 + 0.5469387755t + 3.06122449 + t2 = 0 + 3.06122449 Reorder the terms: -3.06122449 + 3.06122449 + 0.5469387755t + t2 = 0 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + 0.5469387755t + t2 = 0 + 3.06122449 0.5469387755t + t2 = 0 + 3.06122449 Combine like terms: 0 + 3.06122449 = 3.06122449 0.5469387755t + t2 = 3.06122449 The t term is 0.5469387755t. Take half its coefficient (0.2734693878). Square it (0.07478550606) and add it to both sides. Add '0.07478550606' to each side of the equation. 0.5469387755t + 0.07478550606 + t2 = 3.06122449 + 0.07478550606 Reorder the terms: 0.07478550606 + 0.5469387755t + t2 = 3.06122449 + 0.07478550606 Combine like terms: 3.06122449 + 0.07478550606 = 3.13600999606 0.07478550606 + 0.5469387755t + t2 = 3.13600999606 Factor a perfect square on the left side: (t + 0.2734693878)(t + 0.2734693878) = 3.13600999606 Calculate the square root of the right side: 1.770878312 Break this problem into two subproblems by setting (t + 0.2734693878) equal to 1.770878312 and -1.770878312.Subproblem 1
t + 0.2734693878 = 1.770878312 Simplifying t + 0.2734693878 = 1.770878312 Reorder the terms: 0.2734693878 + t = 1.770878312 Solving 0.2734693878 + t = 1.770878312 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2734693878' to each side of the equation. 0.2734693878 + -0.2734693878 + t = 1.770878312 + -0.2734693878 Combine like terms: 0.2734693878 + -0.2734693878 = 0.0000000000 0.0000000000 + t = 1.770878312 + -0.2734693878 t = 1.770878312 + -0.2734693878 Combine like terms: 1.770878312 + -0.2734693878 = 1.4974089242 t = 1.4974089242 Simplifying t = 1.4974089242Subproblem 2
t + 0.2734693878 = -1.770878312 Simplifying t + 0.2734693878 = -1.770878312 Reorder the terms: 0.2734693878 + t = -1.770878312 Solving 0.2734693878 + t = -1.770878312 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2734693878' to each side of the equation. 0.2734693878 + -0.2734693878 + t = -1.770878312 + -0.2734693878 Combine like terms: 0.2734693878 + -0.2734693878 = 0.0000000000 0.0000000000 + t = -1.770878312 + -0.2734693878 t = -1.770878312 + -0.2734693878 Combine like terms: -1.770878312 + -0.2734693878 = -2.0443476998 t = -2.0443476998 Simplifying t = -2.0443476998Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.4974089242, -2.0443476998}
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