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Simplifying -4.9t2 + 18t + 6 = 0 Reorder the terms: 6 + 18t + -4.9t2 = 0 Solving 6 + 18t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -1.224489796 + -3.673469388t + t2 = 0 Move the constant term to the right: Add '1.224489796' to each side of the equation. -1.224489796 + -3.673469388t + 1.224489796 + t2 = 0 + 1.224489796 Reorder the terms: -1.224489796 + 1.224489796 + -3.673469388t + t2 = 0 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + -3.673469388t + t2 = 0 + 1.224489796 -3.673469388t + t2 = 0 + 1.224489796 Combine like terms: 0 + 1.224489796 = 1.224489796 -3.673469388t + t2 = 1.224489796 The t term is -3.673469388t. Take half its coefficient (-1.836734694). Square it (3.373594336) and add it to both sides. Add '3.373594336' to each side of the equation. -3.673469388t + 3.373594336 + t2 = 1.224489796 + 3.373594336 Reorder the terms: 3.373594336 + -3.673469388t + t2 = 1.224489796 + 3.373594336 Combine like terms: 1.224489796 + 3.373594336 = 4.598084132 3.373594336 + -3.673469388t + t2 = 4.598084132 Factor a perfect square on the left side: (t + -1.836734694)(t + -1.836734694) = 4.598084132 Calculate the square root of the right side: 2.144314373 Break this problem into two subproblems by setting (t + -1.836734694) equal to 2.144314373 and -2.144314373.Subproblem 1
t + -1.836734694 = 2.144314373 Simplifying t + -1.836734694 = 2.144314373 Reorder the terms: -1.836734694 + t = 2.144314373 Solving -1.836734694 + t = 2.144314373 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.836734694' to each side of the equation. -1.836734694 + 1.836734694 + t = 2.144314373 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + t = 2.144314373 + 1.836734694 t = 2.144314373 + 1.836734694 Combine like terms: 2.144314373 + 1.836734694 = 3.981049067 t = 3.981049067 Simplifying t = 3.981049067Subproblem 2
t + -1.836734694 = -2.144314373 Simplifying t + -1.836734694 = -2.144314373 Reorder the terms: -1.836734694 + t = -2.144314373 Solving -1.836734694 + t = -2.144314373 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.836734694' to each side of the equation. -1.836734694 + 1.836734694 + t = -2.144314373 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + t = -2.144314373 + 1.836734694 t = -2.144314373 + 1.836734694 Combine like terms: -2.144314373 + 1.836734694 = -0.307579679 t = -0.307579679 Simplifying t = -0.307579679Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.981049067, -0.307579679}
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