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Simplifying 5t2 + 14t = 2 Reorder the terms: 14t + 5t2 = 2 Solving 14t + 5t2 = 2 Solving for variable 't'. Reorder the terms: -2 + 14t + 5t2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 14t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 2.8t + t2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 2.8t + 0.4 + t2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 2.8t + t2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 2.8t + t2 = 0 + 0.4 2.8t + t2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 2.8t + t2 = 0.4 The t term is 2.8t. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8t + 1.96 + t2 = 0.4 + 1.96 Reorder the terms: 1.96 + 2.8t + t2 = 0.4 + 1.96 Combine like terms: 0.4 + 1.96 = 2.36 1.96 + 2.8t + t2 = 2.36 Factor a perfect square on the left side: (t + 1.4)(t + 1.4) = 2.36 Calculate the square root of the right side: 1.53622915 Break this problem into two subproblems by setting (t + 1.4) equal to 1.53622915 and -1.53622915.Subproblem 1
t + 1.4 = 1.53622915 Simplifying t + 1.4 = 1.53622915 Reorder the terms: 1.4 + t = 1.53622915 Solving 1.4 + t = 1.53622915 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + t = 1.53622915 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + t = 1.53622915 + -1.4 t = 1.53622915 + -1.4 Combine like terms: 1.53622915 + -1.4 = 0.13622915 t = 0.13622915 Simplifying t = 0.13622915Subproblem 2
t + 1.4 = -1.53622915 Simplifying t + 1.4 = -1.53622915 Reorder the terms: 1.4 + t = -1.53622915 Solving 1.4 + t = -1.53622915 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + t = -1.53622915 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + t = -1.53622915 + -1.4 t = -1.53622915 + -1.4 Combine like terms: -1.53622915 + -1.4 = -2.93622915 t = -2.93622915 Simplifying t = -2.93622915Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.13622915, -2.93622915}
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