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Simplifying -4.9t2 + 20t + 210 = 0 Reorder the terms: 210 + 20t + -4.9t2 = 0 Solving 210 + 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'. -42.85714286 + -4.081632653t + t2 = 0 Move the constant term to the right: Add '42.85714286' to each side of the equation. -42.85714286 + -4.081632653t + 42.85714286 + t2 = 0 + 42.85714286 Reorder the terms: -42.85714286 + 42.85714286 + -4.081632653t + t2 = 0 + 42.85714286 Combine like terms: -42.85714286 + 42.85714286 = 0.00000000 0.00000000 + -4.081632653t + t2 = 0 + 42.85714286 -4.081632653t + t2 = 0 + 42.85714286 Combine like terms: 0 + 42.85714286 = 42.85714286 -4.081632653t + t2 = 42.85714286 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 = 42.85714286 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653t + t2 = 42.85714286 + 4.164931281 Combine like terms: 42.85714286 + 4.164931281 = 47.022074141 4.164931281 + -4.081632653t + t2 = 47.022074141 Factor a perfect square on the left side: (t + -2.040816327)(t + -2.040816327) = 47.022074141 Calculate the square root of the right side: 6.857264334 Break this problem into two subproblems by setting (t + -2.040816327) equal to 6.857264334 and -6.857264334.Subproblem 1
t + -2.040816327 = 6.857264334 Simplifying t + -2.040816327 = 6.857264334 Reorder the terms: -2.040816327 + t = 6.857264334 Solving -2.040816327 + t = 6.857264334 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 = 6.857264334 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 6.857264334 + 2.040816327 t = 6.857264334 + 2.040816327 Combine like terms: 6.857264334 + 2.040816327 = 8.898080661 t = 8.898080661 Simplifying t = 8.898080661Subproblem 2
t + -2.040816327 = -6.857264334 Simplifying t + -2.040816327 = -6.857264334 Reorder the terms: -2.040816327 + t = -6.857264334 Solving -2.040816327 + t = -6.857264334 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 = -6.857264334 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -6.857264334 + 2.040816327 t = -6.857264334 + 2.040816327 Combine like terms: -6.857264334 + 2.040816327 = -4.816448007 t = -4.816448007 Simplifying t = -4.816448007Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.898080661, -4.816448007}
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