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Simplifying 19t2 + -110t + -190 = 0 Reorder the terms: -190 + -110t + 19t2 = 0 Solving -190 + -110t + 19t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -10 + -5.789473684t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -5.789473684t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -5.789473684t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -5.789473684t + t2 = 0 + 10 -5.789473684t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -5.789473684t + t2 = 10 The t term is -5.789473684t. Take half its coefficient (-2.894736842). Square it (8.379501384) and add it to both sides. Add '8.379501384' to each side of the equation. -5.789473684t + 8.379501384 + t2 = 10 + 8.379501384 Reorder the terms: 8.379501384 + -5.789473684t + t2 = 10 + 8.379501384 Combine like terms: 10 + 8.379501384 = 18.379501384 8.379501384 + -5.789473684t + t2 = 18.379501384 Factor a perfect square on the left side: (t + -2.894736842)(t + -2.894736842) = 18.379501384 Calculate the square root of the right side: 4.28713207 Break this problem into two subproblems by setting (t + -2.894736842) equal to 4.28713207 and -4.28713207.Subproblem 1
t + -2.894736842 = 4.28713207 Simplifying t + -2.894736842 = 4.28713207 Reorder the terms: -2.894736842 + t = 4.28713207 Solving -2.894736842 + t = 4.28713207 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.894736842' to each side of the equation. -2.894736842 + 2.894736842 + t = 4.28713207 + 2.894736842 Combine like terms: -2.894736842 + 2.894736842 = 0.000000000 0.000000000 + t = 4.28713207 + 2.894736842 t = 4.28713207 + 2.894736842 Combine like terms: 4.28713207 + 2.894736842 = 7.181868912 t = 7.181868912 Simplifying t = 7.181868912Subproblem 2
t + -2.894736842 = -4.28713207 Simplifying t + -2.894736842 = -4.28713207 Reorder the terms: -2.894736842 + t = -4.28713207 Solving -2.894736842 + t = -4.28713207 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.894736842' to each side of the equation. -2.894736842 + 2.894736842 + t = -4.28713207 + 2.894736842 Combine like terms: -2.894736842 + 2.894736842 = 0.000000000 0.000000000 + t = -4.28713207 + 2.894736842 t = -4.28713207 + 2.894736842 Combine like terms: -4.28713207 + 2.894736842 = -1.392395228 t = -1.392395228 Simplifying t = -1.392395228Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.181868912, -1.392395228}
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