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Simplifying 4.905t2 + -26.528t + 5 = 0 Reorder the terms: 5 + -26.528t + 4.905t2 = 0 Solving 5 + -26.528t + 4.905t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. 1.019367992 + -5.408358818t + t2 = 0 Move the constant term to the right: Add '-1.019367992' to each side of the equation. 1.019367992 + -5.408358818t + -1.019367992 + t2 = 0 + -1.019367992 Reorder the terms: 1.019367992 + -1.019367992 + -5.408358818t + t2 = 0 + -1.019367992 Combine like terms: 1.019367992 + -1.019367992 = 0.000000000 0.000000000 + -5.408358818t + t2 = 0 + -1.019367992 -5.408358818t + t2 = 0 + -1.019367992 Combine like terms: 0 + -1.019367992 = -1.019367992 -5.408358818t + t2 = -1.019367992 The t term is -5.408358818t. Take half its coefficient (-2.704179409). Square it (7.312586276) and add it to both sides. Add '7.312586276' to each side of the equation. -5.408358818t + 7.312586276 + t2 = -1.019367992 + 7.312586276 Reorder the terms: 7.312586276 + -5.408358818t + t2 = -1.019367992 + 7.312586276 Combine like terms: -1.019367992 + 7.312586276 = 6.293218284 7.312586276 + -5.408358818t + t2 = 6.293218284 Factor a perfect square on the left side: (t + -2.704179409)(t + -2.704179409) = 6.293218284 Calculate the square root of the right side: 2.508628766 Break this problem into two subproblems by setting (t + -2.704179409) equal to 2.508628766 and -2.508628766.Subproblem 1
t + -2.704179409 = 2.508628766 Simplifying t + -2.704179409 = 2.508628766 Reorder the terms: -2.704179409 + t = 2.508628766 Solving -2.704179409 + t = 2.508628766 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.704179409' to each side of the equation. -2.704179409 + 2.704179409 + t = 2.508628766 + 2.704179409 Combine like terms: -2.704179409 + 2.704179409 = 0.000000000 0.000000000 + t = 2.508628766 + 2.704179409 t = 2.508628766 + 2.704179409 Combine like terms: 2.508628766 + 2.704179409 = 5.212808175 t = 5.212808175 Simplifying t = 5.212808175Subproblem 2
t + -2.704179409 = -2.508628766 Simplifying t + -2.704179409 = -2.508628766 Reorder the terms: -2.704179409 + t = -2.508628766 Solving -2.704179409 + t = -2.508628766 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.704179409' to each side of the equation. -2.704179409 + 2.704179409 + t = -2.508628766 + 2.704179409 Combine like terms: -2.704179409 + 2.704179409 = 0.000000000 0.000000000 + t = -2.508628766 + 2.704179409 t = -2.508628766 + 2.704179409 Combine like terms: -2.508628766 + 2.704179409 = 0.195550643 t = 0.195550643 Simplifying t = 0.195550643Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.212808175, 0.195550643}
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