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Simplifying 100 + 20t + -4.9t2 = 0 Solving 100 + 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'. -20.40816327 + -4.081632653t + t2 = 0 Move the constant term to the right: Add '20.40816327' to each side of the equation. -20.40816327 + -4.081632653t + 20.40816327 + t2 = 0 + 20.40816327 Reorder the terms: -20.40816327 + 20.40816327 + -4.081632653t + t2 = 0 + 20.40816327 Combine like terms: -20.40816327 + 20.40816327 = 0.00000000 0.00000000 + -4.081632653t + t2 = 0 + 20.40816327 -4.081632653t + t2 = 0 + 20.40816327 Combine like terms: 0 + 20.40816327 = 20.40816327 -4.081632653t + t2 = 20.40816327 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 = 20.40816327 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653t + t2 = 20.40816327 + 4.164931281 Combine like terms: 20.40816327 + 4.164931281 = 24.573094551 4.164931281 + -4.081632653t + t2 = 24.573094551 Factor a perfect square on the left side: (t + -2.040816327)(t + -2.040816327) = 24.573094551 Calculate the square root of the right side: 4.957125634 Break this problem into two subproblems by setting (t + -2.040816327) equal to 4.957125634 and -4.957125634.Subproblem 1
t + -2.040816327 = 4.957125634 Simplifying t + -2.040816327 = 4.957125634 Reorder the terms: -2.040816327 + t = 4.957125634 Solving -2.040816327 + t = 4.957125634 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 = 4.957125634 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 4.957125634 + 2.040816327 t = 4.957125634 + 2.040816327 Combine like terms: 4.957125634 + 2.040816327 = 6.997941961 t = 6.997941961 Simplifying t = 6.997941961Subproblem 2
t + -2.040816327 = -4.957125634 Simplifying t + -2.040816327 = -4.957125634 Reorder the terms: -2.040816327 + t = -4.957125634 Solving -2.040816327 + t = -4.957125634 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 = -4.957125634 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -4.957125634 + 2.040816327 t = -4.957125634 + 2.040816327 Combine like terms: -4.957125634 + 2.040816327 = -2.916309307 t = -2.916309307 Simplifying t = -2.916309307Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.997941961, -2.916309307}
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