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Simplifying 5t2 + 5t = 1.5 Reorder the terms: 5t + 5t2 = 1.5 Solving 5t + 5t2 = 1.5 Solving for variable 't'. Reorder the terms: -1.5 + 5t + 5t2 = 1.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 -1.5 + 5t + 5t2 = 0.0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.3 + t + t2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + t + 0.3 + t2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + t + t2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + t + t2 = 0.0 + 0.3 t + t2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 t + t2 = 0.3 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 0.3 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 0.3 + 0.25 Combine like terms: 0.3 + 0.25 = 0.55 1.25 + t2 = 0.55 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 0.55 Calculate the square root of the right side: 0.741619849 Break this problem into two subproblems by setting (t + 0.5) equal to 0.741619849 and -0.741619849.Subproblem 1
t + 0.5 = 0.741619849 Simplifying t + 0.5 = 0.741619849 Reorder the terms: 0.5 + t = 0.741619849 Solving 0.5 + t = 0.741619849 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 0.741619849 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 0.741619849 + -0.5 t = 0.741619849 + -0.5 Combine like terms: 0.741619849 + -0.5 = 0.241619849 t = 0.241619849 Simplifying t = 0.241619849Subproblem 2
t + 0.5 = -0.741619849 Simplifying t + 0.5 = -0.741619849 Reorder the terms: 0.5 + t = -0.741619849 Solving 0.5 + t = -0.741619849 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -0.741619849 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -0.741619849 + -0.5 t = -0.741619849 + -0.5 Combine like terms: -0.741619849 + -0.5 = -1.241619849 t = -1.241619849 Simplifying t = -1.241619849Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.241619849, -1.241619849}
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