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Simplifying 14t2 + 15t + -20 = 0 Reorder the terms: -20 + 15t + 14t2 = 0 Solving -20 + 15t + 14t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.428571429 + 1.071428571t + t2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 1.071428571t + 1.428571429 + t2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 1.071428571t + t2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 1.071428571t + t2 = 0 + 1.428571429 1.071428571t + t2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 1.071428571t + t2 = 1.428571429 The t term is 1.071428571t. Take half its coefficient (0.5357142855). Square it (0.2869897957) and add it to both sides. Add '0.2869897957' to each side of the equation. 1.071428571t + 0.2869897957 + t2 = 1.428571429 + 0.2869897957 Reorder the terms: 0.2869897957 + 1.071428571t + t2 = 1.428571429 + 0.2869897957 Combine like terms: 1.428571429 + 0.2869897957 = 1.7155612247 0.2869897957 + 1.071428571t + t2 = 1.7155612247 Factor a perfect square on the left side: (t + 0.5357142855)(t + 0.5357142855) = 1.7155612247 Calculate the square root of the right side: 1.309794344 Break this problem into two subproblems by setting (t + 0.5357142855) equal to 1.309794344 and -1.309794344.Subproblem 1
t + 0.5357142855 = 1.309794344 Simplifying t + 0.5357142855 = 1.309794344 Reorder the terms: 0.5357142855 + t = 1.309794344 Solving 0.5357142855 + t = 1.309794344 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5357142855' to each side of the equation. 0.5357142855 + -0.5357142855 + t = 1.309794344 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + t = 1.309794344 + -0.5357142855 t = 1.309794344 + -0.5357142855 Combine like terms: 1.309794344 + -0.5357142855 = 0.7740800585 t = 0.7740800585 Simplifying t = 0.7740800585Subproblem 2
t + 0.5357142855 = -1.309794344 Simplifying t + 0.5357142855 = -1.309794344 Reorder the terms: 0.5357142855 + t = -1.309794344 Solving 0.5357142855 + t = -1.309794344 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5357142855' to each side of the equation. 0.5357142855 + -0.5357142855 + t = -1.309794344 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + t = -1.309794344 + -0.5357142855 t = -1.309794344 + -0.5357142855 Combine like terms: -1.309794344 + -0.5357142855 = -1.8455086295 t = -1.8455086295 Simplifying t = -1.8455086295Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.7740800585, -1.8455086295}
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