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Simplifying 19.884t2 + -138.744t + 124.26 = 0 Reorder the terms: 124.26 + -138.744t + 19.884t2 = 0 Solving 124.26 + -138.744t + 19.884t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 19.884 the coefficient of the squared term: Divide each side by '19.884'. 6.249245625 + -6.977670489t + t2 = 0 Move the constant term to the right: Add '-6.249245625' to each side of the equation. 6.249245625 + -6.977670489t + -6.249245625 + t2 = 0 + -6.249245625 Reorder the terms: 6.249245625 + -6.249245625 + -6.977670489t + t2 = 0 + -6.249245625 Combine like terms: 6.249245625 + -6.249245625 = 0.000000000 0.000000000 + -6.977670489t + t2 = 0 + -6.249245625 -6.977670489t + t2 = 0 + -6.249245625 Combine like terms: 0 + -6.249245625 = -6.249245625 -6.977670489t + t2 = -6.249245625 The t term is -6.977670489t. Take half its coefficient (-3.488835245). Square it (12.17197137) and add it to both sides. Add '12.17197137' to each side of the equation. -6.977670489t + 12.17197137 + t2 = -6.249245625 + 12.17197137 Reorder the terms: 12.17197137 + -6.977670489t + t2 = -6.249245625 + 12.17197137 Combine like terms: -6.249245625 + 12.17197137 = 5.922725745 12.17197137 + -6.977670489t + t2 = 5.922725745 Factor a perfect square on the left side: (t + -3.488835245)(t + -3.488835245) = 5.922725745 Calculate the square root of the right side: 2.433665085 Break this problem into two subproblems by setting (t + -3.488835245) equal to 2.433665085 and -2.433665085.Subproblem 1
t + -3.488835245 = 2.433665085 Simplifying t + -3.488835245 = 2.433665085 Reorder the terms: -3.488835245 + t = 2.433665085 Solving -3.488835245 + t = 2.433665085 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.488835245' to each side of the equation. -3.488835245 + 3.488835245 + t = 2.433665085 + 3.488835245 Combine like terms: -3.488835245 + 3.488835245 = 0.000000000 0.000000000 + t = 2.433665085 + 3.488835245 t = 2.433665085 + 3.488835245 Combine like terms: 2.433665085 + 3.488835245 = 5.92250033 t = 5.92250033 Simplifying t = 5.92250033Subproblem 2
t + -3.488835245 = -2.433665085 Simplifying t + -3.488835245 = -2.433665085 Reorder the terms: -3.488835245 + t = -2.433665085 Solving -3.488835245 + t = -2.433665085 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.488835245' to each side of the equation. -3.488835245 + 3.488835245 + t = -2.433665085 + 3.488835245 Combine like terms: -3.488835245 + 3.488835245 = 0.000000000 0.000000000 + t = -2.433665085 + 3.488835245 t = -2.433665085 + 3.488835245 Combine like terms: -2.433665085 + 3.488835245 = 1.05517016 t = 1.05517016 Simplifying t = 1.05517016Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.92250033, 1.05517016}
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