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Simplifying 0.0855t2 + -0.916t + 1.737 = 0 Reorder the terms: 1.737 + -0.916t + 0.0855t2 = 0 Solving 1.737 + -0.916t + 0.0855t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0855 the coefficient of the squared term: Divide each side by '0.0855'. 20.31578947 + -10.71345029t + t2 = 0 Move the constant term to the right: Add '-20.31578947' to each side of the equation. 20.31578947 + -10.71345029t + -20.31578947 + t2 = 0 + -20.31578947 Reorder the terms: 20.31578947 + -20.31578947 + -10.71345029t + t2 = 0 + -20.31578947 Combine like terms: 20.31578947 + -20.31578947 = 0.00000000 0.00000000 + -10.71345029t + t2 = 0 + -20.31578947 -10.71345029t + t2 = 0 + -20.31578947 Combine like terms: 0 + -20.31578947 = -20.31578947 -10.71345029t + t2 = -20.31578947 The t term is -10.71345029t. Take half its coefficient (-5.356725145). Square it (28.69450428) and add it to both sides. Add '28.69450428' to each side of the equation. -10.71345029t + 28.69450428 + t2 = -20.31578947 + 28.69450428 Reorder the terms: 28.69450428 + -10.71345029t + t2 = -20.31578947 + 28.69450428 Combine like terms: -20.31578947 + 28.69450428 = 8.37871481 28.69450428 + -10.71345029t + t2 = 8.37871481 Factor a perfect square on the left side: (t + -5.356725145)(t + -5.356725145) = 8.37871481 Calculate the square root of the right side: 2.894600976 Break this problem into two subproblems by setting (t + -5.356725145) equal to 2.894600976 and -2.894600976.Subproblem 1
t + -5.356725145 = 2.894600976 Simplifying t + -5.356725145 = 2.894600976 Reorder the terms: -5.356725145 + t = 2.894600976 Solving -5.356725145 + t = 2.894600976 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.356725145' to each side of the equation. -5.356725145 + 5.356725145 + t = 2.894600976 + 5.356725145 Combine like terms: -5.356725145 + 5.356725145 = 0.000000000 0.000000000 + t = 2.894600976 + 5.356725145 t = 2.894600976 + 5.356725145 Combine like terms: 2.894600976 + 5.356725145 = 8.251326121 t = 8.251326121 Simplifying t = 8.251326121Subproblem 2
t + -5.356725145 = -2.894600976 Simplifying t + -5.356725145 = -2.894600976 Reorder the terms: -5.356725145 + t = -2.894600976 Solving -5.356725145 + t = -2.894600976 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.356725145' to each side of the equation. -5.356725145 + 5.356725145 + t = -2.894600976 + 5.356725145 Combine like terms: -5.356725145 + 5.356725145 = 0.000000000 0.000000000 + t = -2.894600976 + 5.356725145 t = -2.894600976 + 5.356725145 Combine like terms: -2.894600976 + 5.356725145 = 2.462124169 t = 2.462124169 Simplifying t = 2.462124169Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.251326121, 2.462124169}
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