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Simplifying 5t2 + -1t = 20 Reorder the terms: -1t + 5t2 = 20 Solving -1t + 5t2 = 20 Solving for variable 't'. Reorder the terms: -20 + -1t + 5t2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -1t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + -0.2t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.2t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + -0.2t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.2t + t2 = 0 + 4 -0.2t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.2t + t2 = 4 The t term is -0.2t. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2t + 0.01 + t2 = 4 + 0.01 Reorder the terms: 0.01 + -0.2t + t2 = 4 + 0.01 Combine like terms: 4 + 0.01 = 4.01 0.01 + -0.2t + t2 = 4.01 Factor a perfect square on the left side: (t + -0.1)(t + -0.1) = 4.01 Calculate the square root of the right side: 2.002498439 Break this problem into two subproblems by setting (t + -0.1) equal to 2.002498439 and -2.002498439.Subproblem 1
t + -0.1 = 2.002498439 Simplifying t + -0.1 = 2.002498439 Reorder the terms: -0.1 + t = 2.002498439 Solving -0.1 + t = 2.002498439 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + t = 2.002498439 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + t = 2.002498439 + 0.1 t = 2.002498439 + 0.1 Combine like terms: 2.002498439 + 0.1 = 2.102498439 t = 2.102498439 Simplifying t = 2.102498439Subproblem 2
t + -0.1 = -2.002498439 Simplifying t + -0.1 = -2.002498439 Reorder the terms: -0.1 + t = -2.002498439 Solving -0.1 + t = -2.002498439 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + t = -2.002498439 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + t = -2.002498439 + 0.1 t = -2.002498439 + 0.1 Combine like terms: -2.002498439 + 0.1 = -1.902498439 t = -1.902498439 Simplifying t = -1.902498439Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.102498439, -1.902498439}
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