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Simplifying 11t2 + -7t + -100 = 0 Reorder the terms: -100 + -7t + 11t2 = 0 Solving -100 + -7t + 11t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -9.090909091 + -0.6363636364t + t2 = 0 Move the constant term to the right: Add '9.090909091' to each side of the equation. -9.090909091 + -0.6363636364t + 9.090909091 + t2 = 0 + 9.090909091 Reorder the terms: -9.090909091 + 9.090909091 + -0.6363636364t + t2 = 0 + 9.090909091 Combine like terms: -9.090909091 + 9.090909091 = 0.000000000 0.000000000 + -0.6363636364t + t2 = 0 + 9.090909091 -0.6363636364t + t2 = 0 + 9.090909091 Combine like terms: 0 + 9.090909091 = 9.090909091 -0.6363636364t + t2 = 9.090909091 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 = 9.090909091 + 0.1012396694 Reorder the terms: 0.1012396694 + -0.6363636364t + t2 = 9.090909091 + 0.1012396694 Combine like terms: 9.090909091 + 0.1012396694 = 9.1921487604 0.1012396694 + -0.6363636364t + t2 = 9.1921487604 Factor a perfect square on the left side: (t + -0.3181818182)(t + -0.3181818182) = 9.1921487604 Calculate the square root of the right side: 3.031855663 Break this problem into two subproblems by setting (t + -0.3181818182) equal to 3.031855663 and -3.031855663.Subproblem 1
t + -0.3181818182 = 3.031855663 Simplifying t + -0.3181818182 = 3.031855663 Reorder the terms: -0.3181818182 + t = 3.031855663 Solving -0.3181818182 + t = 3.031855663 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 = 3.031855663 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + t = 3.031855663 + 0.3181818182 t = 3.031855663 + 0.3181818182 Combine like terms: 3.031855663 + 0.3181818182 = 3.3500374812 t = 3.3500374812 Simplifying t = 3.3500374812Subproblem 2
t + -0.3181818182 = -3.031855663 Simplifying t + -0.3181818182 = -3.031855663 Reorder the terms: -0.3181818182 + t = -3.031855663 Solving -0.3181818182 + t = -3.031855663 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 = -3.031855663 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + t = -3.031855663 + 0.3181818182 t = -3.031855663 + 0.3181818182 Combine like terms: -3.031855663 + 0.3181818182 = -2.7136738448 t = -2.7136738448 Simplifying t = -2.7136738448Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.3500374812, -2.7136738448}
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