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Simplifying -4.9t2 + 20.38t + 1.2 = 0 Reorder the terms: 1.2 + 20.38t + -4.9t2 = 0 Solving 1.2 + 20.38t + -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'. -0.2448979592 + -4.159183673t + t2 = 0 Move the constant term to the right: Add '0.2448979592' to each side of the equation. -0.2448979592 + -4.159183673t + 0.2448979592 + t2 = 0 + 0.2448979592 Reorder the terms: -0.2448979592 + 0.2448979592 + -4.159183673t + t2 = 0 + 0.2448979592 Combine like terms: -0.2448979592 + 0.2448979592 = 0.0000000000 0.0000000000 + -4.159183673t + t2 = 0 + 0.2448979592 -4.159183673t + t2 = 0 + 0.2448979592 Combine like terms: 0 + 0.2448979592 = 0.2448979592 -4.159183673t + t2 = 0.2448979592 The t term is -4.159183673t. Take half its coefficient (-2.079591837). Square it (4.324702209) and add it to both sides. Add '4.324702209' to each side of the equation. -4.159183673t + 4.324702209 + t2 = 0.2448979592 + 4.324702209 Reorder the terms: 4.324702209 + -4.159183673t + t2 = 0.2448979592 + 4.324702209 Combine like terms: 0.2448979592 + 4.324702209 = 4.5696001682 4.324702209 + -4.159183673t + t2 = 4.5696001682 Factor a perfect square on the left side: (t + -2.079591837)(t + -2.079591837) = 4.5696001682 Calculate the square root of the right side: 2.137662314 Break this problem into two subproblems by setting (t + -2.079591837) equal to 2.137662314 and -2.137662314.Subproblem 1
t + -2.079591837 = 2.137662314 Simplifying t + -2.079591837 = 2.137662314 Reorder the terms: -2.079591837 + t = 2.137662314 Solving -2.079591837 + t = 2.137662314 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.079591837' to each side of the equation. -2.079591837 + 2.079591837 + t = 2.137662314 + 2.079591837 Combine like terms: -2.079591837 + 2.079591837 = 0.000000000 0.000000000 + t = 2.137662314 + 2.079591837 t = 2.137662314 + 2.079591837 Combine like terms: 2.137662314 + 2.079591837 = 4.217254151 t = 4.217254151 Simplifying t = 4.217254151Subproblem 2
t + -2.079591837 = -2.137662314 Simplifying t + -2.079591837 = -2.137662314 Reorder the terms: -2.079591837 + t = -2.137662314 Solving -2.079591837 + t = -2.137662314 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.079591837' to each side of the equation. -2.079591837 + 2.079591837 + t = -2.137662314 + 2.079591837 Combine like terms: -2.079591837 + 2.079591837 = 0.000000000 0.000000000 + t = -2.137662314 + 2.079591837 t = -2.137662314 + 2.079591837 Combine like terms: -2.137662314 + 2.079591837 = -0.058070477 t = -0.058070477 Simplifying t = -0.058070477Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.217254151, -0.058070477}
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