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Simplifying 4.9t2 + -5t + -1.5 = 0 Reorder the terms: -1.5 + -5t + 4.9t2 = 0 Solving -1.5 + -5t + 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'. -0.306122449 + -1.020408163t + t2 = 0 Move the constant term to the right: Add '0.306122449' to each side of the equation. -0.306122449 + -1.020408163t + 0.306122449 + t2 = 0 + 0.306122449 Reorder the terms: -0.306122449 + 0.306122449 + -1.020408163t + t2 = 0 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + -1.020408163t + t2 = 0 + 0.306122449 -1.020408163t + t2 = 0 + 0.306122449 Combine like terms: 0 + 0.306122449 = 0.306122449 -1.020408163t + t2 = 0.306122449 The t term is -1.020408163t. Take half its coefficient (-0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. -1.020408163t + 0.2603082048 + t2 = 0.306122449 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163t + t2 = 0.306122449 + 0.2603082048 Combine like terms: 0.306122449 + 0.2603082048 = 0.5664306538 0.2603082048 + -1.020408163t + t2 = 0.5664306538 Factor a perfect square on the left side: (t + -0.5102040815)(t + -0.5102040815) = 0.5664306538 Calculate the square root of the right side: 0.752615874 Break this problem into two subproblems by setting (t + -0.5102040815) equal to 0.752615874 and -0.752615874.Subproblem 1
t + -0.5102040815 = 0.752615874 Simplifying t + -0.5102040815 = 0.752615874 Reorder the terms: -0.5102040815 + t = 0.752615874 Solving -0.5102040815 + t = 0.752615874 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + t = 0.752615874 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = 0.752615874 + 0.5102040815 t = 0.752615874 + 0.5102040815 Combine like terms: 0.752615874 + 0.5102040815 = 1.2628199555 t = 1.2628199555 Simplifying t = 1.2628199555Subproblem 2
t + -0.5102040815 = -0.752615874 Simplifying t + -0.5102040815 = -0.752615874 Reorder the terms: -0.5102040815 + t = -0.752615874 Solving -0.5102040815 + t = -0.752615874 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + t = -0.752615874 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = -0.752615874 + 0.5102040815 t = -0.752615874 + 0.5102040815 Combine like terms: -0.752615874 + 0.5102040815 = -0.2424117925 t = -0.2424117925 Simplifying t = -0.2424117925Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.2628199555, -0.2424117925}
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