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Simplifying 4.9t2 + -1.0897t + -0.28 = 0 Reorder the terms: -0.28 + -1.0897t + 4.9t2 = 0 Solving -0.28 + -1.0897t + 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'. -0.05714285714 + -0.2223877551t + t2 = 0 Move the constant term to the right: Add '0.05714285714' to each side of the equation. -0.05714285714 + -0.2223877551t + 0.05714285714 + t2 = 0 + 0.05714285714 Reorder the terms: -0.05714285714 + 0.05714285714 + -0.2223877551t + t2 = 0 + 0.05714285714 Combine like terms: -0.05714285714 + 0.05714285714 = 0.00000000000 0.00000000000 + -0.2223877551t + t2 = 0 + 0.05714285714 -0.2223877551t + t2 = 0 + 0.05714285714 Combine like terms: 0 + 0.05714285714 = 0.05714285714 -0.2223877551t + t2 = 0.05714285714 The t term is -0.2223877551t. Take half its coefficient (-0.1111938776). Square it (0.01236407842) and add it to both sides. Add '0.01236407842' to each side of the equation. -0.2223877551t + 0.01236407842 + t2 = 0.05714285714 + 0.01236407842 Reorder the terms: 0.01236407842 + -0.2223877551t + t2 = 0.05714285714 + 0.01236407842 Combine like terms: 0.05714285714 + 0.01236407842 = 0.06950693556 0.01236407842 + -0.2223877551t + t2 = 0.06950693556 Factor a perfect square on the left side: (t + -0.1111938776)(t + -0.1111938776) = 0.06950693556 Calculate the square root of the right side: 0.26364168 Break this problem into two subproblems by setting (t + -0.1111938776) equal to 0.26364168 and -0.26364168.Subproblem 1
t + -0.1111938776 = 0.26364168 Simplifying t + -0.1111938776 = 0.26364168 Reorder the terms: -0.1111938776 + t = 0.26364168 Solving -0.1111938776 + t = 0.26364168 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1111938776' to each side of the equation. -0.1111938776 + 0.1111938776 + t = 0.26364168 + 0.1111938776 Combine like terms: -0.1111938776 + 0.1111938776 = 0.0000000000 0.0000000000 + t = 0.26364168 + 0.1111938776 t = 0.26364168 + 0.1111938776 Combine like terms: 0.26364168 + 0.1111938776 = 0.3748355576 t = 0.3748355576 Simplifying t = 0.3748355576Subproblem 2
t + -0.1111938776 = -0.26364168 Simplifying t + -0.1111938776 = -0.26364168 Reorder the terms: -0.1111938776 + t = -0.26364168 Solving -0.1111938776 + t = -0.26364168 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1111938776' to each side of the equation. -0.1111938776 + 0.1111938776 + t = -0.26364168 + 0.1111938776 Combine like terms: -0.1111938776 + 0.1111938776 = 0.0000000000 0.0000000000 + t = -0.26364168 + 0.1111938776 t = -0.26364168 + 0.1111938776 Combine like terms: -0.26364168 + 0.1111938776 = -0.1524478024 t = -0.1524478024 Simplifying t = -0.1524478024Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.3748355576, -0.1524478024}
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