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Simplifying -4.9t2 + 20.38t + 2.3 = 0 Reorder the terms: 2.3 + 20.38t + -4.9t2 = 0 Solving 2.3 + 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'. -0.4693877551 + -4.159183673t + t2 = 0 Move the constant term to the right: Add '0.4693877551' to each side of the equation. -0.4693877551 + -4.159183673t + 0.4693877551 + t2 = 0 + 0.4693877551 Reorder the terms: -0.4693877551 + 0.4693877551 + -4.159183673t + t2 = 0 + 0.4693877551 Combine like terms: -0.4693877551 + 0.4693877551 = 0.0000000000 0.0000000000 + -4.159183673t + t2 = 0 + 0.4693877551 -4.159183673t + t2 = 0 + 0.4693877551 Combine like terms: 0 + 0.4693877551 = 0.4693877551 -4.159183673t + t2 = 0.4693877551 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 = 0.4693877551 + 4.324702209 Reorder the terms: 4.324702209 + -4.159183673t + t2 = 0.4693877551 + 4.324702209 Combine like terms: 0.4693877551 + 4.324702209 = 4.7940899641 4.324702209 + -4.159183673t + t2 = 4.7940899641 Factor a perfect square on the left side: (t + -2.079591837)(t + -2.079591837) = 4.7940899641 Calculate the square root of the right side: 2.18954104 Break this problem into two subproblems by setting (t + -2.079591837) equal to 2.18954104 and -2.18954104.Subproblem 1
t + -2.079591837 = 2.18954104 Simplifying t + -2.079591837 = 2.18954104 Reorder the terms: -2.079591837 + t = 2.18954104 Solving -2.079591837 + t = 2.18954104 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 = 2.18954104 + 2.079591837 Combine like terms: -2.079591837 + 2.079591837 = 0.000000000 0.000000000 + t = 2.18954104 + 2.079591837 t = 2.18954104 + 2.079591837 Combine like terms: 2.18954104 + 2.079591837 = 4.269132877 t = 4.269132877 Simplifying t = 4.269132877Subproblem 2
t + -2.079591837 = -2.18954104 Simplifying t + -2.079591837 = -2.18954104 Reorder the terms: -2.079591837 + t = -2.18954104 Solving -2.079591837 + t = -2.18954104 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 = -2.18954104 + 2.079591837 Combine like terms: -2.079591837 + 2.079591837 = 0.000000000 0.000000000 + t = -2.18954104 + 2.079591837 t = -2.18954104 + 2.079591837 Combine like terms: -2.18954104 + 2.079591837 = -0.109949203 t = -0.109949203 Simplifying t = -0.109949203Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.269132877, -0.109949203}
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