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Simplifying (5t2 + -9) + -1(8t + 13) = 0 Reorder the terms: (-9 + 5t2) + -1(8t + 13) = 0 Remove parenthesis around (-9 + 5t2) -9 + 5t2 + -1(8t + 13) = 0 Reorder the terms: -9 + 5t2 + -1(13 + 8t) = 0 -9 + 5t2 + (13 * -1 + 8t * -1) = 0 -9 + 5t2 + (-13 + -8t) = 0 Reorder the terms: -9 + -13 + -8t + 5t2 = 0 Combine like terms: -9 + -13 = -22 -22 + -8t + 5t2 = 0 Solving -22 + -8t + 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'. -4.4 + -1.6t + t2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + -1.6t + 4.4 + t2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + -1.6t + t2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + -1.6t + t2 = 0 + 4.4 -1.6t + t2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 -1.6t + t2 = 4.4 The t term is -1.6t. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6t + 0.64 + t2 = 4.4 + 0.64 Reorder the terms: 0.64 + -1.6t + t2 = 4.4 + 0.64 Combine like terms: 4.4 + 0.64 = 5.04 0.64 + -1.6t + t2 = 5.04 Factor a perfect square on the left side: (t + -0.8)(t + -0.8) = 5.04 Calculate the square root of the right side: 2.244994432 Break this problem into two subproblems by setting (t + -0.8) equal to 2.244994432 and -2.244994432.Subproblem 1
t + -0.8 = 2.244994432 Simplifying t + -0.8 = 2.244994432 Reorder the terms: -0.8 + t = 2.244994432 Solving -0.8 + t = 2.244994432 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + t = 2.244994432 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + t = 2.244994432 + 0.8 t = 2.244994432 + 0.8 Combine like terms: 2.244994432 + 0.8 = 3.044994432 t = 3.044994432 Simplifying t = 3.044994432Subproblem 2
t + -0.8 = -2.244994432 Simplifying t + -0.8 = -2.244994432 Reorder the terms: -0.8 + t = -2.244994432 Solving -0.8 + t = -2.244994432 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + t = -2.244994432 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + t = -2.244994432 + 0.8 t = -2.244994432 + 0.8 Combine like terms: -2.244994432 + 0.8 = -1.444994432 t = -1.444994432 Simplifying t = -1.444994432Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.044994432, -1.444994432}
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