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Simplifying 5t2 + -54t + -26 = 0 Reorder the terms: -26 + -54t + 5t2 = 0 Solving -26 + -54t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.2 + -10.8t + t2 = 0 Move the constant term to the right: Add '5.2' to each side of the equation. -5.2 + -10.8t + 5.2 + t2 = 0 + 5.2 Reorder the terms: -5.2 + 5.2 + -10.8t + t2 = 0 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + -10.8t + t2 = 0 + 5.2 -10.8t + t2 = 0 + 5.2 Combine like terms: 0 + 5.2 = 5.2 -10.8t + t2 = 5.2 The t term is -10.8t. Take half its coefficient (-5.4). Square it (29.16) and add it to both sides. Add '29.16' to each side of the equation. -10.8t + 29.16 + t2 = 5.2 + 29.16 Reorder the terms: 29.16 + -10.8t + t2 = 5.2 + 29.16 Combine like terms: 5.2 + 29.16 = 34.36 29.16 + -10.8t + t2 = 34.36 Factor a perfect square on the left side: (t + -5.4)(t + -5.4) = 34.36 Calculate the square root of the right side: 5.861740356 Break this problem into two subproblems by setting (t + -5.4) equal to 5.861740356 and -5.861740356.Subproblem 1
t + -5.4 = 5.861740356 Simplifying t + -5.4 = 5.861740356 Reorder the terms: -5.4 + t = 5.861740356 Solving -5.4 + t = 5.861740356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.4' to each side of the equation. -5.4 + 5.4 + t = 5.861740356 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + t = 5.861740356 + 5.4 t = 5.861740356 + 5.4 Combine like terms: 5.861740356 + 5.4 = 11.261740356 t = 11.261740356 Simplifying t = 11.261740356Subproblem 2
t + -5.4 = -5.861740356 Simplifying t + -5.4 = -5.861740356 Reorder the terms: -5.4 + t = -5.861740356 Solving -5.4 + t = -5.861740356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.4' to each side of the equation. -5.4 + 5.4 + t = -5.861740356 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + t = -5.861740356 + 5.4 t = -5.861740356 + 5.4 Combine like terms: -5.861740356 + 5.4 = -0.461740356 t = -0.461740356 Simplifying t = -0.461740356Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.261740356, -0.461740356}
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