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Simplifying 56t2 + -19t = 56 Reorder the terms: -19t + 56t2 = 56 Solving -19t + 56t2 = 56 Solving for variable 't'. Reorder the terms: -56 + -19t + 56t2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + -19t + 56t2 = 0 Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. -1 + -0.3392857143t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.3392857143t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -0.3392857143t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.3392857143t + t2 = 0 + 1 -0.3392857143t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.3392857143t + t2 = 1 The t term is -0.3392857143t. Take half its coefficient (-0.1696428572). Square it (0.02877869900) and add it to both sides. Add '0.02877869900' to each side of the equation. -0.3392857143t + 0.02877869900 + t2 = 1 + 0.02877869900 Reorder the terms: 0.02877869900 + -0.3392857143t + t2 = 1 + 0.02877869900 Combine like terms: 1 + 0.02877869900 = 1.028778699 0.02877869900 + -0.3392857143t + t2 = 1.028778699 Factor a perfect square on the left side: (t + -0.1696428572)(t + -0.1696428572) = 1.028778699 Calculate the square root of the right side: 1.014287286 Break this problem into two subproblems by setting (t + -0.1696428572) equal to 1.014287286 and -1.014287286.Subproblem 1
t + -0.1696428572 = 1.014287286 Simplifying t + -0.1696428572 = 1.014287286 Reorder the terms: -0.1696428572 + t = 1.014287286 Solving -0.1696428572 + t = 1.014287286 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1696428572' to each side of the equation. -0.1696428572 + 0.1696428572 + t = 1.014287286 + 0.1696428572 Combine like terms: -0.1696428572 + 0.1696428572 = 0.0000000000 0.0000000000 + t = 1.014287286 + 0.1696428572 t = 1.014287286 + 0.1696428572 Combine like terms: 1.014287286 + 0.1696428572 = 1.1839301432 t = 1.1839301432 Simplifying t = 1.1839301432Subproblem 2
t + -0.1696428572 = -1.014287286 Simplifying t + -0.1696428572 = -1.014287286 Reorder the terms: -0.1696428572 + t = -1.014287286 Solving -0.1696428572 + t = -1.014287286 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1696428572' to each side of the equation. -0.1696428572 + 0.1696428572 + t = -1.014287286 + 0.1696428572 Combine like terms: -0.1696428572 + 0.1696428572 = 0.0000000000 0.0000000000 + t = -1.014287286 + 0.1696428572 t = -1.014287286 + 0.1696428572 Combine like terms: -1.014287286 + 0.1696428572 = -0.8446444288 t = -0.8446444288 Simplifying t = -0.8446444288Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.1839301432, -0.8446444288}
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