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Simplifying -4.9t2 + 20t + 20 = 0 Reorder the terms: 20 + 20t + -4.9t2 = 0 Solving 20 + 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'. -4.081632653 + -4.081632653t + t2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + -4.081632653t + 4.081632653 + t2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + -4.081632653t + t2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + -4.081632653t + t2 = 0 + 4.081632653 -4.081632653t + t2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 -4.081632653t + t2 = 4.081632653 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 = 4.081632653 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653t + t2 = 4.081632653 + 4.164931281 Combine like terms: 4.081632653 + 4.164931281 = 8.246563934 4.164931281 + -4.081632653t + t2 = 8.246563934 Factor a perfect square on the left side: (t + -2.040816327)(t + -2.040816327) = 8.246563934 Calculate the square root of the right side: 2.871683119 Break this problem into two subproblems by setting (t + -2.040816327) equal to 2.871683119 and -2.871683119.Subproblem 1
t + -2.040816327 = 2.871683119 Simplifying t + -2.040816327 = 2.871683119 Reorder the terms: -2.040816327 + t = 2.871683119 Solving -2.040816327 + t = 2.871683119 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 = 2.871683119 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 2.871683119 + 2.040816327 t = 2.871683119 + 2.040816327 Combine like terms: 2.871683119 + 2.040816327 = 4.912499446 t = 4.912499446 Simplifying t = 4.912499446Subproblem 2
t + -2.040816327 = -2.871683119 Simplifying t + -2.040816327 = -2.871683119 Reorder the terms: -2.040816327 + t = -2.871683119 Solving -2.040816327 + t = -2.871683119 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 = -2.871683119 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -2.871683119 + 2.040816327 t = -2.871683119 + 2.040816327 Combine like terms: -2.871683119 + 2.040816327 = -0.830866792 t = -0.830866792 Simplifying t = -0.830866792Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.912499446, -0.830866792}
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