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Simplifying -4.9t2 + 5.5t + 15 = 0 Reorder the terms: 15 + 5.5t + -4.9t2 = 0 Solving 15 + 5.5t + -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'. -3.06122449 + -1.12244898t + t2 = 0 Move the constant term to the right: Add '3.06122449' to each side of the equation. -3.06122449 + -1.12244898t + 3.06122449 + t2 = 0 + 3.06122449 Reorder the terms: -3.06122449 + 3.06122449 + -1.12244898t + t2 = 0 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + -1.12244898t + t2 = 0 + 3.06122449 -1.12244898t + t2 = 0 + 3.06122449 Combine like terms: 0 + 3.06122449 = 3.06122449 -1.12244898t + t2 = 3.06122449 The t term is -1.12244898t. Take half its coefficient (-0.56122449). Square it (0.3149729282) and add it to both sides. Add '0.3149729282' to each side of the equation. -1.12244898t + 0.3149729282 + t2 = 3.06122449 + 0.3149729282 Reorder the terms: 0.3149729282 + -1.12244898t + t2 = 3.06122449 + 0.3149729282 Combine like terms: 3.06122449 + 0.3149729282 = 3.3761974182 0.3149729282 + -1.12244898t + t2 = 3.3761974182 Factor a perfect square on the left side: (t + -0.56122449)(t + -0.56122449) = 3.3761974182 Calculate the square root of the right side: 1.837443174 Break this problem into two subproblems by setting (t + -0.56122449) equal to 1.837443174 and -1.837443174.Subproblem 1
t + -0.56122449 = 1.837443174 Simplifying t + -0.56122449 = 1.837443174 Reorder the terms: -0.56122449 + t = 1.837443174 Solving -0.56122449 + t = 1.837443174 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.56122449' to each side of the equation. -0.56122449 + 0.56122449 + t = 1.837443174 + 0.56122449 Combine like terms: -0.56122449 + 0.56122449 = 0.00000000 0.00000000 + t = 1.837443174 + 0.56122449 t = 1.837443174 + 0.56122449 Combine like terms: 1.837443174 + 0.56122449 = 2.398667664 t = 2.398667664 Simplifying t = 2.398667664Subproblem 2
t + -0.56122449 = -1.837443174 Simplifying t + -0.56122449 = -1.837443174 Reorder the terms: -0.56122449 + t = -1.837443174 Solving -0.56122449 + t = -1.837443174 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.56122449' to each side of the equation. -0.56122449 + 0.56122449 + t = -1.837443174 + 0.56122449 Combine like terms: -0.56122449 + 0.56122449 = 0.00000000 0.00000000 + t = -1.837443174 + 0.56122449 t = -1.837443174 + 0.56122449 Combine like terms: -1.837443174 + 0.56122449 = -1.276218684 t = -1.276218684 Simplifying t = -1.276218684Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.398667664, -1.276218684}
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