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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 = 3.9200333218 4.164931281 + 4.081632653t + t2 = 3.9200333218 Factor a perfect square on the left side: (t + 2.040816327)(t + 2.040816327) = 3.9200333218 Calculate the square root of the right side: 1.979907402 Break this problem into two subproblems by setting (t + 2.040816327) equal to 1.979907402 and -1.979907402.Subproblem 1
t + 2.040816327 = 1.979907402 Simplifying t + 2.040816327 = 1.979907402 Reorder the terms: 2.040816327 + t = 1.979907402 Solving 2.040816327 + t = 1.979907402 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 = 1.979907402 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = 1.979907402 + -2.040816327 t = 1.979907402 + -2.040816327 Combine like terms: 1.979907402 + -2.040816327 = -0.060908925 t = -0.060908925 Simplifying t = -0.060908925Subproblem 2
t + 2.040816327 = -1.979907402 Simplifying t + 2.040816327 = -1.979907402 Reorder the terms: 2.040816327 + t = -1.979907402 Solving 2.040816327 + t = -1.979907402 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 = -1.979907402 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = -1.979907402 + -2.040816327 t = -1.979907402 + -2.040816327 Combine like terms: -1.979907402 + -2.040816327 = -4.020723729 t = -4.020723729 Simplifying t = -4.020723729Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.060908925, -4.020723729}
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