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Simplifying 4.9t2 + -2.89t + -8.09 = 0 Reorder the terms: -8.09 + -2.89t + 4.9t2 = 0 Solving -8.09 + -2.89t + 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'. -1.651020408 + -0.5897959184t + t2 = 0 Move the constant term to the right: Add '1.651020408' to each side of the equation. -1.651020408 + -0.5897959184t + 1.651020408 + t2 = 0 + 1.651020408 Reorder the terms: -1.651020408 + 1.651020408 + -0.5897959184t + t2 = 0 + 1.651020408 Combine like terms: -1.651020408 + 1.651020408 = 0.000000000 0.000000000 + -0.5897959184t + t2 = 0 + 1.651020408 -0.5897959184t + t2 = 0 + 1.651020408 Combine like terms: 0 + 1.651020408 = 1.651020408 -0.5897959184t + t2 = 1.651020408 The t term is -0.5897959184t. Take half its coefficient (-0.2948979592). Square it (0.08696480634) and add it to both sides. Add '0.08696480634' to each side of the equation. -0.5897959184t + 0.08696480634 + t2 = 1.651020408 + 0.08696480634 Reorder the terms: 0.08696480634 + -0.5897959184t + t2 = 1.651020408 + 0.08696480634 Combine like terms: 1.651020408 + 0.08696480634 = 1.73798521434 0.08696480634 + -0.5897959184t + t2 = 1.73798521434 Factor a perfect square on the left side: (t + -0.2948979592)(t + -0.2948979592) = 1.73798521434 Calculate the square root of the right side: 1.318326672 Break this problem into two subproblems by setting (t + -0.2948979592) equal to 1.318326672 and -1.318326672.Subproblem 1
t + -0.2948979592 = 1.318326672 Simplifying t + -0.2948979592 = 1.318326672 Reorder the terms: -0.2948979592 + t = 1.318326672 Solving -0.2948979592 + t = 1.318326672 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2948979592' to each side of the equation. -0.2948979592 + 0.2948979592 + t = 1.318326672 + 0.2948979592 Combine like terms: -0.2948979592 + 0.2948979592 = 0.0000000000 0.0000000000 + t = 1.318326672 + 0.2948979592 t = 1.318326672 + 0.2948979592 Combine like terms: 1.318326672 + 0.2948979592 = 1.6132246312 t = 1.6132246312 Simplifying t = 1.6132246312Subproblem 2
t + -0.2948979592 = -1.318326672 Simplifying t + -0.2948979592 = -1.318326672 Reorder the terms: -0.2948979592 + t = -1.318326672 Solving -0.2948979592 + t = -1.318326672 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2948979592' to each side of the equation. -0.2948979592 + 0.2948979592 + t = -1.318326672 + 0.2948979592 Combine like terms: -0.2948979592 + 0.2948979592 = 0.0000000000 0.0000000000 + t = -1.318326672 + 0.2948979592 t = -1.318326672 + 0.2948979592 Combine like terms: -1.318326672 + 0.2948979592 = -1.0234287128 t = -1.0234287128 Simplifying t = -1.0234287128Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.6132246312, -1.0234287128}
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