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Simplifying 25 = 23t + -5t2 Solving 25 = 23t + -5t2 Solving for variable 't'. Reorder the terms: 25 + -23t + 5t2 = 23t + -23t + -5t2 + 5t2 Combine like terms: 23t + -23t = 0 25 + -23t + 5t2 = 0 + -5t2 + 5t2 25 + -23t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 25 + -23t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5 + -4.6t + t2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -4.6t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + -4.6t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4.6t + t2 = 0 + -5 -4.6t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 -4.6t + t2 = -5 The t term is -4.6t. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6t + 5.29 + t2 = -5 + 5.29 Reorder the terms: 5.29 + -4.6t + t2 = -5 + 5.29 Combine like terms: -5 + 5.29 = 0.29 5.29 + -4.6t + t2 = 0.29 Factor a perfect square on the left side: (t + -2.3)(t + -2.3) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (t + -2.3) equal to 0.538516481 and -0.538516481.Subproblem 1
t + -2.3 = 0.538516481 Simplifying t + -2.3 = 0.538516481 Reorder the terms: -2.3 + t = 0.538516481 Solving -2.3 + t = 0.538516481 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + t = 0.538516481 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + t = 0.538516481 + 2.3 t = 0.538516481 + 2.3 Combine like terms: 0.538516481 + 2.3 = 2.838516481 t = 2.838516481 Simplifying t = 2.838516481Subproblem 2
t + -2.3 = -0.538516481 Simplifying t + -2.3 = -0.538516481 Reorder the terms: -2.3 + t = -0.538516481 Solving -2.3 + t = -0.538516481 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + t = -0.538516481 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + t = -0.538516481 + 2.3 t = -0.538516481 + 2.3 Combine like terms: -0.538516481 + 2.3 = 1.761483519 t = 1.761483519 Simplifying t = 1.761483519Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.838516481, 1.761483519}
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