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Simplifying 11t2 = 7t + 10 Reorder the terms: 11t2 = 10 + 7t Solving 11t2 = 10 + 7t Solving for variable 't'. Reorder the terms: -10 + -7t + 11t2 = 10 + 7t + -10 + -7t Reorder the terms: -10 + -7t + 11t2 = 10 + -10 + 7t + -7t Combine like terms: 10 + -10 = 0 -10 + -7t + 11t2 = 0 + 7t + -7t -10 + -7t + 11t2 = 7t + -7t Combine like terms: 7t + -7t = 0 -10 + -7t + 11t2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.9090909091 + -0.6363636364t + t2 = 0 Move the constant term to the right: Add '0.9090909091' to each side of the equation. -0.9090909091 + -0.6363636364t + 0.9090909091 + t2 = 0 + 0.9090909091 Reorder the terms: -0.9090909091 + 0.9090909091 + -0.6363636364t + t2 = 0 + 0.9090909091 Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000 0.0000000000 + -0.6363636364t + t2 = 0 + 0.9090909091 -0.6363636364t + t2 = 0 + 0.9090909091 Combine like terms: 0 + 0.9090909091 = 0.9090909091 -0.6363636364t + t2 = 0.9090909091 The t term is -0.6363636364t. Take half its coefficient (-0.3181818182). Square it (0.1012396694) and add it to both sides. Add '0.1012396694' to each side of the equation. -0.6363636364t + 0.1012396694 + t2 = 0.9090909091 + 0.1012396694 Reorder the terms: 0.1012396694 + -0.6363636364t + t2 = 0.9090909091 + 0.1012396694 Combine like terms: 0.9090909091 + 0.1012396694 = 1.0103305785 0.1012396694 + -0.6363636364t + t2 = 1.0103305785 Factor a perfect square on the left side: (t + -0.3181818182)(t + -0.3181818182) = 1.0103305785 Calculate the square root of the right side: 1.005152018 Break this problem into two subproblems by setting (t + -0.3181818182) equal to 1.005152018 and -1.005152018.Subproblem 1
t + -0.3181818182 = 1.005152018 Simplifying t + -0.3181818182 = 1.005152018 Reorder the terms: -0.3181818182 + t = 1.005152018 Solving -0.3181818182 + t = 1.005152018 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + t = 1.005152018 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + t = 1.005152018 + 0.3181818182 t = 1.005152018 + 0.3181818182 Combine like terms: 1.005152018 + 0.3181818182 = 1.3233338362 t = 1.3233338362 Simplifying t = 1.3233338362Subproblem 2
t + -0.3181818182 = -1.005152018 Simplifying t + -0.3181818182 = -1.005152018 Reorder the terms: -0.3181818182 + t = -1.005152018 Solving -0.3181818182 + t = -1.005152018 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + t = -1.005152018 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + t = -1.005152018 + 0.3181818182 t = -1.005152018 + 0.3181818182 Combine like terms: -1.005152018 + 0.3181818182 = -0.6869701998 t = -0.6869701998 Simplifying t = -0.6869701998Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.3233338362, -0.6869701998}
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