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Simplifying 4.9t2 + 20t + -12 = 0 Reorder the terms: -12 + 20t + 4.9t2 = 0 Solving -12 + 20t + 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'. -2.448979592 + 4.081632653t + t2 = 0 Move the constant term to the right: Add '2.448979592' to each side of the equation. -2.448979592 + 4.081632653t + 2.448979592 + t2 = 0 + 2.448979592 Reorder the terms: -2.448979592 + 2.448979592 + 4.081632653t + t2 = 0 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + 4.081632653t + t2 = 0 + 2.448979592 4.081632653t + t2 = 0 + 2.448979592 Combine like terms: 0 + 2.448979592 = 2.448979592 4.081632653t + t2 = 2.448979592 The t term is 4.081632653t. Take half its coefficient (2.040816327). Square it (4.164931281) and add it to both sides. Add '4.164931281' to each side of the equation. 4.081632653t + 4.164931281 + t2 = 2.448979592 + 4.164931281 Reorder the terms: 4.164931281 + 4.081632653t + t2 = 2.448979592 + 4.164931281 Combine like terms: 2.448979592 + 4.164931281 = 6.613910873 4.164931281 + 4.081632653t + t2 = 6.613910873 Factor a perfect square on the left side: (t + 2.040816327)(t + 2.040816327) = 6.613910873 Calculate the square root of the right side: 2.571752491 Break this problem into two subproblems by setting (t + 2.040816327) equal to 2.571752491 and -2.571752491.Subproblem 1
t + 2.040816327 = 2.571752491 Simplifying t + 2.040816327 = 2.571752491 Reorder the terms: 2.040816327 + t = 2.571752491 Solving 2.040816327 + t = 2.571752491 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.040816327' to each side of the equation. 2.040816327 + -2.040816327 + t = 2.571752491 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = 2.571752491 + -2.040816327 t = 2.571752491 + -2.040816327 Combine like terms: 2.571752491 + -2.040816327 = 0.530936164 t = 0.530936164 Simplifying t = 0.530936164Subproblem 2
t + 2.040816327 = -2.571752491 Simplifying t + 2.040816327 = -2.571752491 Reorder the terms: 2.040816327 + t = -2.571752491 Solving 2.040816327 + t = -2.571752491 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.040816327' to each side of the equation. 2.040816327 + -2.040816327 + t = -2.571752491 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = -2.571752491 + -2.040816327 t = -2.571752491 + -2.040816327 Combine like terms: -2.571752491 + -2.040816327 = -4.612568818 t = -4.612568818 Simplifying t = -4.612568818Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.530936164, -4.612568818}
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