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Simplifying 5t2 + -13t + -16 = 0 Reorder the terms: -16 + -13t + 5t2 = 0 Solving -16 + -13t + 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'. -3.2 + -2.6t + t2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -2.6t + 3.2 + t2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -2.6t + t2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -2.6t + t2 = 0 + 3.2 -2.6t + t2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -2.6t + t2 = 3.2 The t term is -2.6t. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6t + 1.69 + t2 = 3.2 + 1.69 Reorder the terms: 1.69 + -2.6t + t2 = 3.2 + 1.69 Combine like terms: 3.2 + 1.69 = 4.89 1.69 + -2.6t + t2 = 4.89 Factor a perfect square on the left side: (t + -1.3)(t + -1.3) = 4.89 Calculate the square root of the right side: 2.211334439 Break this problem into two subproblems by setting (t + -1.3) equal to 2.211334439 and -2.211334439.Subproblem 1
t + -1.3 = 2.211334439 Simplifying t + -1.3 = 2.211334439 Reorder the terms: -1.3 + t = 2.211334439 Solving -1.3 + t = 2.211334439 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + t = 2.211334439 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + t = 2.211334439 + 1.3 t = 2.211334439 + 1.3 Combine like terms: 2.211334439 + 1.3 = 3.511334439 t = 3.511334439 Simplifying t = 3.511334439Subproblem 2
t + -1.3 = -2.211334439 Simplifying t + -1.3 = -2.211334439 Reorder the terms: -1.3 + t = -2.211334439 Solving -1.3 + t = -2.211334439 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + t = -2.211334439 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + t = -2.211334439 + 1.3 t = -2.211334439 + 1.3 Combine like terms: -2.211334439 + 1.3 = -0.911334439 t = -0.911334439 Simplifying t = -0.911334439Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.511334439, -0.911334439}
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