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Simplifying -3 + -15t + 5t2 = 0 Solving -3 + -15t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -3t + t2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -3t + 0.6 + t2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -3t + t2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -3t + t2 = 0 + 0.6 -3t + t2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -3t + t2 = 0.6 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 = 0.6 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 0.6 + 2.25 Combine like terms: 0.6 + 2.25 = 2.85 2.25 + -3t + t2 = 2.85 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 2.85 Calculate the square root of the right side: 1.688194302 Break this problem into two subproblems by setting (t + -1.5) equal to 1.688194302 and -1.688194302.Subproblem 1
t + -1.5 = 1.688194302 Simplifying t + -1.5 = 1.688194302 Reorder the terms: -1.5 + t = 1.688194302 Solving -1.5 + t = 1.688194302 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 = 1.688194302 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 1.688194302 + 1.5 t = 1.688194302 + 1.5 Combine like terms: 1.688194302 + 1.5 = 3.188194302 t = 3.188194302 Simplifying t = 3.188194302Subproblem 2
t + -1.5 = -1.688194302 Simplifying t + -1.5 = -1.688194302 Reorder the terms: -1.5 + t = -1.688194302 Solving -1.5 + t = -1.688194302 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 = -1.688194302 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -1.688194302 + 1.5 t = -1.688194302 + 1.5 Combine like terms: -1.688194302 + 1.5 = -0.188194302 t = -0.188194302 Simplifying t = -0.188194302Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.188194302, -0.188194302}
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