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Simplifying 2t2 + 2t = 3 Reorder the terms: 2t + 2t2 = 3 Solving 2t + 2t2 = 3 Solving for variable 't'. Reorder the terms: -3 + 2t + 2t2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 2t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + t + t2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + t + 1.5 + t2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + t + t2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t + t2 = 0 + 1.5 t + t2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 t + t2 = 1.5 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 = 1.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 1.5 + 0.25 Combine like terms: 1.5 + 0.25 = 1.75 1.25 + t2 = 1.75 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (t + 0.5) equal to 1.322875656 and -1.322875656.Subproblem 1
t + 0.5 = 1.322875656 Simplifying t + 0.5 = 1.322875656 Reorder the terms: 0.5 + t = 1.322875656 Solving 0.5 + t = 1.322875656 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 = 1.322875656 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 1.322875656 + -0.5 t = 1.322875656 + -0.5 Combine like terms: 1.322875656 + -0.5 = 0.822875656 t = 0.822875656 Simplifying t = 0.822875656Subproblem 2
t + 0.5 = -1.322875656 Simplifying t + 0.5 = -1.322875656 Reorder the terms: 0.5 + t = -1.322875656 Solving 0.5 + t = -1.322875656 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 = -1.322875656 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -1.322875656 + -0.5 t = -1.322875656 + -0.5 Combine like terms: -1.322875656 + -0.5 = -1.822875656 t = -1.822875656 Simplifying t = -1.822875656Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.822875656, -1.822875656}
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