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Simplifying 1 = 18t + 5t2 Solving 1 = 18t + 5t2 Solving for variable 't'. Reorder the terms: 1 + -18t + -5t2 = 18t + -18t + 5t2 + -5t2 Combine like terms: 18t + -18t = 0 1 + -18t + -5t2 = 0 + 5t2 + -5t2 1 + -18t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 1 + -18t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.2 + 3.6t + t2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 3.6t + 0.2 + t2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 3.6t + t2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 3.6t + t2 = 0 + 0.2 3.6t + t2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 3.6t + t2 = 0.2 The t term is 3.6t. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6t + 3.24 + t2 = 0.2 + 3.24 Reorder the terms: 3.24 + 3.6t + t2 = 0.2 + 3.24 Combine like terms: 0.2 + 3.24 = 3.44 3.24 + 3.6t + t2 = 3.44 Factor a perfect square on the left side: (t + 1.8)(t + 1.8) = 3.44 Calculate the square root of the right side: 1.854723699 Break this problem into two subproblems by setting (t + 1.8) equal to 1.854723699 and -1.854723699.Subproblem 1
t + 1.8 = 1.854723699 Simplifying t + 1.8 = 1.854723699 Reorder the terms: 1.8 + t = 1.854723699 Solving 1.8 + t = 1.854723699 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + t = 1.854723699 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + t = 1.854723699 + -1.8 t = 1.854723699 + -1.8 Combine like terms: 1.854723699 + -1.8 = 0.054723699 t = 0.054723699 Simplifying t = 0.054723699Subproblem 2
t + 1.8 = -1.854723699 Simplifying t + 1.8 = -1.854723699 Reorder the terms: 1.8 + t = -1.854723699 Solving 1.8 + t = -1.854723699 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + t = -1.854723699 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + t = -1.854723699 + -1.8 t = -1.854723699 + -1.8 Combine like terms: -1.854723699 + -1.8 = -3.654723699 t = -3.654723699 Simplifying t = -3.654723699Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.054723699, -3.654723699}
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