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Simplifying 2 + 28t + -4.9t2 = 0 Solving 2 + 28t + -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'. -0.4081632653 + -5.714285714t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -5.714285714t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -5.714285714t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -5.714285714t + t2 = 0 + 0.4081632653 -5.714285714t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -5.714285714t + t2 = 0.4081632653 The t term is -5.714285714t. Take half its coefficient (-2.857142857). Square it (8.163265305) and add it to both sides. Add '8.163265305' to each side of the equation. -5.714285714t + 8.163265305 + t2 = 0.4081632653 + 8.163265305 Reorder the terms: 8.163265305 + -5.714285714t + t2 = 0.4081632653 + 8.163265305 Combine like terms: 0.4081632653 + 8.163265305 = 8.5714285703 8.163265305 + -5.714285714t + t2 = 8.5714285703 Factor a perfect square on the left side: (t + -2.857142857)(t + -2.857142857) = 8.5714285703 Calculate the square root of the right side: 2.927700219 Break this problem into two subproblems by setting (t + -2.857142857) equal to 2.927700219 and -2.927700219.Subproblem 1
t + -2.857142857 = 2.927700219 Simplifying t + -2.857142857 = 2.927700219 Reorder the terms: -2.857142857 + t = 2.927700219 Solving -2.857142857 + t = 2.927700219 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.857142857' to each side of the equation. -2.857142857 + 2.857142857 + t = 2.927700219 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + t = 2.927700219 + 2.857142857 t = 2.927700219 + 2.857142857 Combine like terms: 2.927700219 + 2.857142857 = 5.784843076 t = 5.784843076 Simplifying t = 5.784843076Subproblem 2
t + -2.857142857 = -2.927700219 Simplifying t + -2.857142857 = -2.927700219 Reorder the terms: -2.857142857 + t = -2.927700219 Solving -2.857142857 + t = -2.927700219 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.857142857' to each side of the equation. -2.857142857 + 2.857142857 + t = -2.927700219 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + t = -2.927700219 + 2.857142857 t = -2.927700219 + 2.857142857 Combine like terms: -2.927700219 + 2.857142857 = -0.070557362 t = -0.070557362 Simplifying t = -0.070557362Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.784843076, -0.070557362}
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