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Simplifying 0 = t2 + 2.92t + -2.14 Reorder the terms: 0 = -2.14 + 2.92t + t2 Solving 0 = -2.14 + 2.92t + t2 Solving for variable 't'. Combine like terms: 0 + 2.14 = 2.14 2.14 + -2.92t + -1t2 = -2.14 + 2.92t + t2 + 2.14 + -2.92t + -1t2 Reorder the terms: 2.14 + -2.92t + -1t2 = -2.14 + 2.14 + 2.92t + -2.92t + t2 + -1t2 Combine like terms: -2.14 + 2.14 = 0.00 2.14 + -2.92t + -1t2 = 0.00 + 2.92t + -2.92t + t2 + -1t2 2.14 + -2.92t + -1t2 = 2.92t + -2.92t + t2 + -1t2 Combine like terms: 2.92t + -2.92t = 0.00 2.14 + -2.92t + -1t2 = 0.00 + t2 + -1t2 2.14 + -2.92t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 2.14 + -2.92t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2.14 + 2.92t + t2 = 0 Move the constant term to the right: Add '2.14' to each side of the equation. -2.14 + 2.92t + 2.14 + t2 = 0 + 2.14 Reorder the terms: -2.14 + 2.14 + 2.92t + t2 = 0 + 2.14 Combine like terms: -2.14 + 2.14 = 0.00 0.00 + 2.92t + t2 = 0 + 2.14 2.92t + t2 = 0 + 2.14 Combine like terms: 0 + 2.14 = 2.14 2.92t + t2 = 2.14 The t term is 2.92t. Take half its coefficient (1.46). Square it (2.1316) and add it to both sides. Add '2.1316' to each side of the equation. 2.92t + 2.1316 + t2 = 2.14 + 2.1316 Reorder the terms: 2.1316 + 2.92t + t2 = 2.14 + 2.1316 Combine like terms: 2.14 + 2.1316 = 4.2716 2.1316 + 2.92t + t2 = 4.2716 Factor a perfect square on the left side: (t + 1.46)(t + 1.46) = 4.2716 Calculate the square root of the right side: 2.066784943 Break this problem into two subproblems by setting (t + 1.46) equal to 2.066784943 and -2.066784943.Subproblem 1
t + 1.46 = 2.066784943 Simplifying t + 1.46 = 2.066784943 Reorder the terms: 1.46 + t = 2.066784943 Solving 1.46 + t = 2.066784943 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.46' to each side of the equation. 1.46 + -1.46 + t = 2.066784943 + -1.46 Combine like terms: 1.46 + -1.46 = 0.00 0.00 + t = 2.066784943 + -1.46 t = 2.066784943 + -1.46 Combine like terms: 2.066784943 + -1.46 = 0.606784943 t = 0.606784943 Simplifying t = 0.606784943Subproblem 2
t + 1.46 = -2.066784943 Simplifying t + 1.46 = -2.066784943 Reorder the terms: 1.46 + t = -2.066784943 Solving 1.46 + t = -2.066784943 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.46' to each side of the equation. 1.46 + -1.46 + t = -2.066784943 + -1.46 Combine like terms: 1.46 + -1.46 = 0.00 0.00 + t = -2.066784943 + -1.46 t = -2.066784943 + -1.46 Combine like terms: -2.066784943 + -1.46 = -3.526784943 t = -3.526784943 Simplifying t = -3.526784943Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.606784943, -3.526784943}
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