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Simplifying 2t2 + -18t + -5 = 0 Reorder the terms: -5 + -18t + 2t2 = 0 Solving -5 + -18t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -9t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -9t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -9t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -9t + t2 = 0 + 2.5 -9t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -9t + t2 = 2.5 The t term is -9t. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9t + 20.25 + t2 = 2.5 + 20.25 Reorder the terms: 20.25 + -9t + t2 = 2.5 + 20.25 Combine like terms: 2.5 + 20.25 = 22.75 20.25 + -9t + t2 = 22.75 Factor a perfect square on the left side: (t + -4.5)(t + -4.5) = 22.75 Calculate the square root of the right side: 4.769696007 Break this problem into two subproblems by setting (t + -4.5) equal to 4.769696007 and -4.769696007.Subproblem 1
t + -4.5 = 4.769696007 Simplifying t + -4.5 = 4.769696007 Reorder the terms: -4.5 + t = 4.769696007 Solving -4.5 + t = 4.769696007 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = 4.769696007 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = 4.769696007 + 4.5 t = 4.769696007 + 4.5 Combine like terms: 4.769696007 + 4.5 = 9.269696007 t = 9.269696007 Simplifying t = 9.269696007Subproblem 2
t + -4.5 = -4.769696007 Simplifying t + -4.5 = -4.769696007 Reorder the terms: -4.5 + t = -4.769696007 Solving -4.5 + t = -4.769696007 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = -4.769696007 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = -4.769696007 + 4.5 t = -4.769696007 + 4.5 Combine like terms: -4.769696007 + 4.5 = -0.269696007 t = -0.269696007 Simplifying t = -0.269696007Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.269696007, -0.269696007}
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