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Simplifying -4.9t2 + 5.5t + 120 = 0 Reorder the terms: 120 + 5.5t + -4.9t2 = 0 Solving 120 + 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'. -24.48979592 + -1.12244898t + t2 = 0 Move the constant term to the right: Add '24.48979592' to each side of the equation. -24.48979592 + -1.12244898t + 24.48979592 + t2 = 0 + 24.48979592 Reorder the terms: -24.48979592 + 24.48979592 + -1.12244898t + t2 = 0 + 24.48979592 Combine like terms: -24.48979592 + 24.48979592 = 0.00000000 0.00000000 + -1.12244898t + t2 = 0 + 24.48979592 -1.12244898t + t2 = 0 + 24.48979592 Combine like terms: 0 + 24.48979592 = 24.48979592 -1.12244898t + t2 = 24.48979592 The t term is -1.12244898t. Take half its coefficient (-0.56122449). Square it (0.3149729282) and add it to both sides. Add '0.3149729282' to each side of the equation. -1.12244898t + 0.3149729282 + t2 = 24.48979592 + 0.3149729282 Reorder the terms: 0.3149729282 + -1.12244898t + t2 = 24.48979592 + 0.3149729282 Combine like terms: 24.48979592 + 0.3149729282 = 24.8047688482 0.3149729282 + -1.12244898t + t2 = 24.8047688482 Factor a perfect square on the left side: (t + -0.56122449)(t + -0.56122449) = 24.8047688482 Calculate the square root of the right side: 4.98043862 Break this problem into two subproblems by setting (t + -0.56122449) equal to 4.98043862 and -4.98043862.Subproblem 1
t + -0.56122449 = 4.98043862 Simplifying t + -0.56122449 = 4.98043862 Reorder the terms: -0.56122449 + t = 4.98043862 Solving -0.56122449 + t = 4.98043862 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.56122449' to each side of the equation. -0.56122449 + 0.56122449 + t = 4.98043862 + 0.56122449 Combine like terms: -0.56122449 + 0.56122449 = 0.00000000 0.00000000 + t = 4.98043862 + 0.56122449 t = 4.98043862 + 0.56122449 Combine like terms: 4.98043862 + 0.56122449 = 5.54166311 t = 5.54166311 Simplifying t = 5.54166311Subproblem 2
t + -0.56122449 = -4.98043862 Simplifying t + -0.56122449 = -4.98043862 Reorder the terms: -0.56122449 + t = -4.98043862 Solving -0.56122449 + t = -4.98043862 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.56122449' to each side of the equation. -0.56122449 + 0.56122449 + t = -4.98043862 + 0.56122449 Combine like terms: -0.56122449 + 0.56122449 = 0.00000000 0.00000000 + t = -4.98043862 + 0.56122449 t = -4.98043862 + 0.56122449 Combine like terms: -4.98043862 + 0.56122449 = -4.41921413 t = -4.41921413 Simplifying t = -4.41921413Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.54166311, -4.41921413}
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