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Simplifying 5t2 + -17t + 20 = 19 Reorder the terms: 20 + -17t + 5t2 = 19 Solving 20 + -17t + 5t2 = 19 Solving for variable 't'. Reorder the terms: 20 + -19 + -17t + 5t2 = 19 + -19 Combine like terms: 20 + -19 = 1 1 + -17t + 5t2 = 19 + -19 Combine like terms: 19 + -19 = 0 1 + -17t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -3.4t + t2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -3.4t + -0.2 + t2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -3.4t + t2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -3.4t + t2 = 0 + -0.2 -3.4t + t2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -3.4t + t2 = -0.2 The t term is -3.4t. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4t + 2.89 + t2 = -0.2 + 2.89 Reorder the terms: 2.89 + -3.4t + t2 = -0.2 + 2.89 Combine like terms: -0.2 + 2.89 = 2.69 2.89 + -3.4t + t2 = 2.69 Factor a perfect square on the left side: (t + -1.7)(t + -1.7) = 2.69 Calculate the square root of the right side: 1.640121947 Break this problem into two subproblems by setting (t + -1.7) equal to 1.640121947 and -1.640121947.Subproblem 1
t + -1.7 = 1.640121947 Simplifying t + -1.7 = 1.640121947 Reorder the terms: -1.7 + t = 1.640121947 Solving -1.7 + t = 1.640121947 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + t = 1.640121947 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + t = 1.640121947 + 1.7 t = 1.640121947 + 1.7 Combine like terms: 1.640121947 + 1.7 = 3.340121947 t = 3.340121947 Simplifying t = 3.340121947Subproblem 2
t + -1.7 = -1.640121947 Simplifying t + -1.7 = -1.640121947 Reorder the terms: -1.7 + t = -1.640121947 Solving -1.7 + t = -1.640121947 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + t = -1.640121947 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + t = -1.640121947 + 1.7 t = -1.640121947 + 1.7 Combine like terms: -1.640121947 + 1.7 = 0.059878053 t = 0.059878053 Simplifying t = 0.059878053Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.340121947, 0.059878053}
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