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Simplifying 4.9t2 + -4.0669t + -0.28 = 0 Reorder the terms: -0.28 + -4.0669t + 4.9t2 = 0 Solving -0.28 + -4.0669t + 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 + -0.8299795918t + t2 = 0 Move the constant term to the right: Add '0.05714285714' to each side of the equation. -0.05714285714 + -0.8299795918t + 0.05714285714 + t2 = 0 + 0.05714285714 Reorder the terms: -0.05714285714 + 0.05714285714 + -0.8299795918t + t2 = 0 + 0.05714285714 Combine like terms: -0.05714285714 + 0.05714285714 = 0.00000000000 0.00000000000 + -0.8299795918t + t2 = 0 + 0.05714285714 -0.8299795918t + t2 = 0 + 0.05714285714 Combine like terms: 0 + 0.05714285714 = 0.05714285714 -0.8299795918t + t2 = 0.05714285714 The t term is -0.8299795918t. Take half its coefficient (-0.4149897959). Square it (0.1722165307) and add it to both sides. Add '0.1722165307' to each side of the equation. -0.8299795918t + 0.1722165307 + t2 = 0.05714285714 + 0.1722165307 Reorder the terms: 0.1722165307 + -0.8299795918t + t2 = 0.05714285714 + 0.1722165307 Combine like terms: 0.05714285714 + 0.1722165307 = 0.22935938784 0.1722165307 + -0.8299795918t + t2 = 0.22935938784 Factor a perfect square on the left side: (t + -0.4149897959)(t + -0.4149897959) = 0.22935938784 Calculate the square root of the right side: 0.478914802 Break this problem into two subproblems by setting (t + -0.4149897959) equal to 0.478914802 and -0.478914802.Subproblem 1
t + -0.4149897959 = 0.478914802 Simplifying t + -0.4149897959 = 0.478914802 Reorder the terms: -0.4149897959 + t = 0.478914802 Solving -0.4149897959 + t = 0.478914802 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4149897959' to each side of the equation. -0.4149897959 + 0.4149897959 + t = 0.478914802 + 0.4149897959 Combine like terms: -0.4149897959 + 0.4149897959 = 0.0000000000 0.0000000000 + t = 0.478914802 + 0.4149897959 t = 0.478914802 + 0.4149897959 Combine like terms: 0.478914802 + 0.4149897959 = 0.8939045979 t = 0.8939045979 Simplifying t = 0.8939045979Subproblem 2
t + -0.4149897959 = -0.478914802 Simplifying t + -0.4149897959 = -0.478914802 Reorder the terms: -0.4149897959 + t = -0.478914802 Solving -0.4149897959 + t = -0.478914802 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4149897959' to each side of the equation. -0.4149897959 + 0.4149897959 + t = -0.478914802 + 0.4149897959 Combine like terms: -0.4149897959 + 0.4149897959 = 0.0000000000 0.0000000000 + t = -0.478914802 + 0.4149897959 t = -0.478914802 + 0.4149897959 Combine like terms: -0.478914802 + 0.4149897959 = -0.0639250061 t = -0.0639250061 Simplifying t = -0.0639250061Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.8939045979, -0.0639250061}
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