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Simplifying -2t2 + 5t + 4 = 0 Reorder the terms: 4 + 5t + -2t2 = 0 Solving 4 + 5t + -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 + -2.5t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.5t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -2.5t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.5t + t2 = 0 + 2 -2.5t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.5t + t2 = 2 The t term is -2.5t. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5t + 1.5625 + t2 = 2 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = 2 + 1.5625 Combine like terms: 2 + 1.5625 = 3.5625 1.5625 + -2.5t + t2 = 3.5625 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (t + -1.25) equal to 1.887458609 and -1.887458609.Subproblem 1
t + -1.25 = 1.887458609 Simplifying t + -1.25 = 1.887458609 Reorder the terms: -1.25 + t = 1.887458609 Solving -1.25 + t = 1.887458609 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = 1.887458609 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 1.887458609 + 1.25 t = 1.887458609 + 1.25 Combine like terms: 1.887458609 + 1.25 = 3.137458609 t = 3.137458609 Simplifying t = 3.137458609Subproblem 2
t + -1.25 = -1.887458609 Simplifying t + -1.25 = -1.887458609 Reorder the terms: -1.25 + t = -1.887458609 Solving -1.25 + t = -1.887458609 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = -1.887458609 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -1.887458609 + 1.25 t = -1.887458609 + 1.25 Combine like terms: -1.887458609 + 1.25 = -0.637458609 t = -0.637458609 Simplifying t = -0.637458609Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.137458609, -0.637458609}
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