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Simplifying -2t2 + -6t + 5 = 0 Reorder the terms: 5 + -6t + -2t2 = 0 Solving 5 + -6t + -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 + 3t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 3t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 3t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 3t + t2 = 0 + 2.5 3t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 3t + t2 = 2.5 The t term is 3t. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3t + 2.25 + t2 = 2.5 + 2.25 Reorder the terms: 2.25 + 3t + t2 = 2.5 + 2.25 Combine like terms: 2.5 + 2.25 = 4.75 2.25 + 3t + t2 = 4.75 Factor a perfect square on the left side: (t + 1.5)(t + 1.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (t + 1.5) equal to 2.179449472 and -2.179449472.Subproblem 1
t + 1.5 = 2.179449472 Simplifying t + 1.5 = 2.179449472 Reorder the terms: 1.5 + t = 2.179449472 Solving 1.5 + t = 2.179449472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = 2.179449472 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = 2.179449472 + -1.5 t = 2.179449472 + -1.5 Combine like terms: 2.179449472 + -1.5 = 0.679449472 t = 0.679449472 Simplifying t = 0.679449472Subproblem 2
t + 1.5 = -2.179449472 Simplifying t + 1.5 = -2.179449472 Reorder the terms: 1.5 + t = -2.179449472 Solving 1.5 + t = -2.179449472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = -2.179449472 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = -2.179449472 + -1.5 t = -2.179449472 + -1.5 Combine like terms: -2.179449472 + -1.5 = -3.679449472 t = -3.679449472 Simplifying t = -3.679449472Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.679449472, -3.679449472}
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