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Simplifying -4.9t2 + 20t + 65 = 0 Reorder the terms: 65 + 20t + -4.9t2 = 0 Solving 65 + 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'. -13.26530612 + -4.081632653t + t2 = 0 Move the constant term to the right: Add '13.26530612' to each side of the equation. -13.26530612 + -4.081632653t + 13.26530612 + t2 = 0 + 13.26530612 Reorder the terms: -13.26530612 + 13.26530612 + -4.081632653t + t2 = 0 + 13.26530612 Combine like terms: -13.26530612 + 13.26530612 = 0.00000000 0.00000000 + -4.081632653t + t2 = 0 + 13.26530612 -4.081632653t + t2 = 0 + 13.26530612 Combine like terms: 0 + 13.26530612 = 13.26530612 -4.081632653t + t2 = 13.26530612 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 = 13.26530612 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653t + t2 = 13.26530612 + 4.164931281 Combine like terms: 13.26530612 + 4.164931281 = 17.430237401 4.164931281 + -4.081632653t + t2 = 17.430237401 Factor a perfect square on the left side: (t + -2.040816327)(t + -2.040816327) = 17.430237401 Calculate the square root of the right side: 4.174953581 Break this problem into two subproblems by setting (t + -2.040816327) equal to 4.174953581 and -4.174953581.Subproblem 1
t + -2.040816327 = 4.174953581 Simplifying t + -2.040816327 = 4.174953581 Reorder the terms: -2.040816327 + t = 4.174953581 Solving -2.040816327 + t = 4.174953581 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 = 4.174953581 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 4.174953581 + 2.040816327 t = 4.174953581 + 2.040816327 Combine like terms: 4.174953581 + 2.040816327 = 6.215769908 t = 6.215769908 Simplifying t = 6.215769908Subproblem 2
t + -2.040816327 = -4.174953581 Simplifying t + -2.040816327 = -4.174953581 Reorder the terms: -2.040816327 + t = -4.174953581 Solving -2.040816327 + t = -4.174953581 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 = -4.174953581 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -4.174953581 + 2.040816327 t = -4.174953581 + 2.040816327 Combine like terms: -4.174953581 + 2.040816327 = -2.134137254 t = -2.134137254 Simplifying t = -2.134137254Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.215769908, -2.134137254}
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