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Simplifying 0.0795t2 + -0.884t + 1.798 = 0 Reorder the terms: 1.798 + -0.884t + 0.0795t2 = 0 Solving 1.798 + -0.884t + 0.0795t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0795 the coefficient of the squared term: Divide each side by '0.0795'. 22.6163522 + -11.11949686t + t2 = 0 Move the constant term to the right: Add '-22.6163522' to each side of the equation. 22.6163522 + -11.11949686t + -22.6163522 + t2 = 0 + -22.6163522 Reorder the terms: 22.6163522 + -22.6163522 + -11.11949686t + t2 = 0 + -22.6163522 Combine like terms: 22.6163522 + -22.6163522 = 0.0000000 0.0000000 + -11.11949686t + t2 = 0 + -22.6163522 -11.11949686t + t2 = 0 + -22.6163522 Combine like terms: 0 + -22.6163522 = -22.6163522 -11.11949686t + t2 = -22.6163522 The t term is -11.11949686t. Take half its coefficient (-5.55974843). Square it (30.91080260) and add it to both sides. Add '30.91080260' to each side of the equation. -11.11949686t + 30.91080260 + t2 = -22.6163522 + 30.91080260 Reorder the terms: 30.91080260 + -11.11949686t + t2 = -22.6163522 + 30.91080260 Combine like terms: -22.6163522 + 30.91080260 = 8.2944504 30.91080260 + -11.11949686t + t2 = 8.2944504 Factor a perfect square on the left side: (t + -5.55974843)(t + -5.55974843) = 8.2944504 Calculate the square root of the right side: 2.88000875 Break this problem into two subproblems by setting (t + -5.55974843) equal to 2.88000875 and -2.88000875.Subproblem 1
t + -5.55974843 = 2.88000875 Simplifying t + -5.55974843 = 2.88000875 Reorder the terms: -5.55974843 + t = 2.88000875 Solving -5.55974843 + t = 2.88000875 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.55974843' to each side of the equation. -5.55974843 + 5.55974843 + t = 2.88000875 + 5.55974843 Combine like terms: -5.55974843 + 5.55974843 = 0.00000000 0.00000000 + t = 2.88000875 + 5.55974843 t = 2.88000875 + 5.55974843 Combine like terms: 2.88000875 + 5.55974843 = 8.43975718 t = 8.43975718 Simplifying t = 8.43975718Subproblem 2
t + -5.55974843 = -2.88000875 Simplifying t + -5.55974843 = -2.88000875 Reorder the terms: -5.55974843 + t = -2.88000875 Solving -5.55974843 + t = -2.88000875 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.55974843' to each side of the equation. -5.55974843 + 5.55974843 + t = -2.88000875 + 5.55974843 Combine like terms: -5.55974843 + 5.55974843 = 0.00000000 0.00000000 + t = -2.88000875 + 5.55974843 t = -2.88000875 + 5.55974843 Combine like terms: -2.88000875 + 5.55974843 = 2.67973968 t = 2.67973968 Simplifying t = 2.67973968Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.43975718, 2.67973968}
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