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Simplifying 4.9t2 + -2.9772t + -0.28 = 0 Reorder the terms: -0.28 + -2.9772t + 4.9t2 = 0 Solving -0.28 + -2.9772t + 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 + -0.6075918367t + t2 = 0 Move the constant term to the right: Add '0.05714285714' to each side of the equation. -0.05714285714 + -0.6075918367t + 0.05714285714 + t2 = 0 + 0.05714285714 Reorder the terms: -0.05714285714 + 0.05714285714 + -0.6075918367t + t2 = 0 + 0.05714285714 Combine like terms: -0.05714285714 + 0.05714285714 = 0.00000000000 0.00000000000 + -0.6075918367t + t2 = 0 + 0.05714285714 -0.6075918367t + t2 = 0 + 0.05714285714 Combine like terms: 0 + 0.05714285714 = 0.05714285714 -0.6075918367t + t2 = 0.05714285714 The t term is -0.6075918367t. Take half its coefficient (-0.3037959184). Square it (0.09229196004) and add it to both sides. Add '0.09229196004' to each side of the equation. -0.6075918367t + 0.09229196004 + t2 = 0.05714285714 + 0.09229196004 Reorder the terms: 0.09229196004 + -0.6075918367t + t2 = 0.05714285714 + 0.09229196004 Combine like terms: 0.05714285714 + 0.09229196004 = 0.14943481718 0.09229196004 + -0.6075918367t + t2 = 0.14943481718 Factor a perfect square on the left side: (t + -0.3037959184)(t + -0.3037959184) = 0.14943481718 Calculate the square root of the right side: 0.386567998 Break this problem into two subproblems by setting (t + -0.3037959184) equal to 0.386567998 and -0.386567998.Subproblem 1
t + -0.3037959184 = 0.386567998 Simplifying t + -0.3037959184 = 0.386567998 Reorder the terms: -0.3037959184 + t = 0.386567998 Solving -0.3037959184 + t = 0.386567998 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3037959184' to each side of the equation. -0.3037959184 + 0.3037959184 + t = 0.386567998 + 0.3037959184 Combine like terms: -0.3037959184 + 0.3037959184 = 0.0000000000 0.0000000000 + t = 0.386567998 + 0.3037959184 t = 0.386567998 + 0.3037959184 Combine like terms: 0.386567998 + 0.3037959184 = 0.6903639164 t = 0.6903639164 Simplifying t = 0.6903639164Subproblem 2
t + -0.3037959184 = -0.386567998 Simplifying t + -0.3037959184 = -0.386567998 Reorder the terms: -0.3037959184 + t = -0.386567998 Solving -0.3037959184 + t = -0.386567998 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3037959184' to each side of the equation. -0.3037959184 + 0.3037959184 + t = -0.386567998 + 0.3037959184 Combine like terms: -0.3037959184 + 0.3037959184 = 0.0000000000 0.0000000000 + t = -0.386567998 + 0.3037959184 t = -0.386567998 + 0.3037959184 Combine like terms: -0.386567998 + 0.3037959184 = -0.0827720796 t = -0.0827720796 Simplifying t = -0.0827720796Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.6903639164, -0.0827720796}
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