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Simplifying 4.9t2 + -2.14t + -0.26 = 0 Reorder the terms: -0.26 + -2.14t + 4.9t2 = 0 Solving -0.26 + -2.14t + 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'. -0.05306122449 + -0.4367346939t + t2 = 0 Move the constant term to the right: Add '0.05306122449' to each side of the equation. -0.05306122449 + -0.4367346939t + 0.05306122449 + t2 = 0 + 0.05306122449 Reorder the terms: -0.05306122449 + 0.05306122449 + -0.4367346939t + t2 = 0 + 0.05306122449 Combine like terms: -0.05306122449 + 0.05306122449 = 0.00000000000 0.00000000000 + -0.4367346939t + t2 = 0 + 0.05306122449 -0.4367346939t + t2 = 0 + 0.05306122449 Combine like terms: 0 + 0.05306122449 = 0.05306122449 -0.4367346939t + t2 = 0.05306122449 The t term is -0.4367346939t. Take half its coefficient (-0.218367347). Square it (0.04768429824) and add it to both sides. Add '0.04768429824' to each side of the equation. -0.4367346939t + 0.04768429824 + t2 = 0.05306122449 + 0.04768429824 Reorder the terms: 0.04768429824 + -0.4367346939t + t2 = 0.05306122449 + 0.04768429824 Combine like terms: 0.05306122449 + 0.04768429824 = 0.10074552273 0.04768429824 + -0.4367346939t + t2 = 0.10074552273 Factor a perfect square on the left side: (t + -0.218367347)(t + -0.218367347) = 0.10074552273 Calculate the square root of the right side: 0.317404352 Break this problem into two subproblems by setting (t + -0.218367347) equal to 0.317404352 and -0.317404352.Subproblem 1
t + -0.218367347 = 0.317404352 Simplifying t + -0.218367347 = 0.317404352 Reorder the terms: -0.218367347 + t = 0.317404352 Solving -0.218367347 + t = 0.317404352 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.218367347' to each side of the equation. -0.218367347 + 0.218367347 + t = 0.317404352 + 0.218367347 Combine like terms: -0.218367347 + 0.218367347 = 0.000000000 0.000000000 + t = 0.317404352 + 0.218367347 t = 0.317404352 + 0.218367347 Combine like terms: 0.317404352 + 0.218367347 = 0.535771699 t = 0.535771699 Simplifying t = 0.535771699Subproblem 2
t + -0.218367347 = -0.317404352 Simplifying t + -0.218367347 = -0.317404352 Reorder the terms: -0.218367347 + t = -0.317404352 Solving -0.218367347 + t = -0.317404352 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.218367347' to each side of the equation. -0.218367347 + 0.218367347 + t = -0.317404352 + 0.218367347 Combine like terms: -0.218367347 + 0.218367347 = 0.000000000 0.000000000 + t = -0.317404352 + 0.218367347 t = -0.317404352 + 0.218367347 Combine like terms: -0.317404352 + 0.218367347 = -0.099037005 t = -0.099037005 Simplifying t = -0.099037005Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.535771699, -0.099037005}
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