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Simplifying 0 = -4.9t * t + 20t + 1.2 Multiply t * t 0 = -4.9t2 + 20t + 1.2 Reorder the terms: 0 = 1.2 + 20t + -4.9t2 Solving 0 = 1.2 + 20t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -1.2 = -1.2 -1.2 + -20t + 4.9t2 = 1.2 + 20t + -4.9t2 + -1.2 + -20t + 4.9t2 Reorder the terms: -1.2 + -20t + 4.9t2 = 1.2 + -1.2 + 20t + -20t + -4.9t2 + 4.9t2 Combine like terms: 1.2 + -1.2 = 0.0 -1.2 + -20t + 4.9t2 = 0.0 + 20t + -20t + -4.9t2 + 4.9t2 -1.2 + -20t + 4.9t2 = 20t + -20t + -4.9t2 + 4.9t2 Combine like terms: 20t + -20t = 0 -1.2 + -20t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -1.2 + -20t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -1.2 + -20t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.2448979592 + -4.081632653t + t2 = 0 Move the constant term to the right: Add '0.2448979592' to each side of the equation. -0.2448979592 + -4.081632653t + 0.2448979592 + t2 = 0 + 0.2448979592 Reorder the terms: -0.2448979592 + 0.2448979592 + -4.081632653t + t2 = 0 + 0.2448979592 Combine like terms: -0.2448979592 + 0.2448979592 = 0.0000000000 0.0000000000 + -4.081632653t + t2 = 0 + 0.2448979592 -4.081632653t + t2 = 0 + 0.2448979592 Combine like terms: 0 + 0.2448979592 = 0.2448979592 -4.081632653t + t2 = 0.2448979592 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 = 0.2448979592 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653t + t2 = 0.2448979592 + 4.164931281 Combine like terms: 0.2448979592 + 4.164931281 = 4.4098292402 4.164931281 + -4.081632653t + t2 = 4.4098292402 Factor a perfect square on the left side: (t + -2.040816327)(t + -2.040816327) = 4.4098292402 Calculate the square root of the right side: 2.099959343 Break this problem into two subproblems by setting (t + -2.040816327) equal to 2.099959343 and -2.099959343.Subproblem 1
t + -2.040816327 = 2.099959343 Simplifying t + -2.040816327 = 2.099959343 Reorder the terms: -2.040816327 + t = 2.099959343 Solving -2.040816327 + t = 2.099959343 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 = 2.099959343 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 2.099959343 + 2.040816327 t = 2.099959343 + 2.040816327 Combine like terms: 2.099959343 + 2.040816327 = 4.14077567 t = 4.14077567 Simplifying t = 4.14077567Subproblem 2
t + -2.040816327 = -2.099959343 Simplifying t + -2.040816327 = -2.099959343 Reorder the terms: -2.040816327 + t = -2.099959343 Solving -2.040816327 + t = -2.099959343 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 = -2.099959343 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -2.099959343 + 2.040816327 t = -2.099959343 + 2.040816327 Combine like terms: -2.099959343 + 2.040816327 = -0.059143016 t = -0.059143016 Simplifying t = -0.059143016Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.14077567, -0.059143016}
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