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Simplifying 160 + 3t + -1t2 = 0 Solving 160 + 3t + -1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -160 + -3t + t2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + -3t + 160 + t2 = 0 + 160 Reorder the terms: -160 + 160 + -3t + t2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -3t + t2 = 0 + 160 -3t + t2 = 0 + 160 Combine like terms: 0 + 160 = 160 -3t + t2 = 160 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 = 160 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 160 + 2.25 Combine like terms: 160 + 2.25 = 162.25 2.25 + -3t + t2 = 162.25 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 162.25 Calculate the square root of the right side: 12.737739203 Break this problem into two subproblems by setting (t + -1.5) equal to 12.737739203 and -12.737739203.Subproblem 1
t + -1.5 = 12.737739203 Simplifying t + -1.5 = 12.737739203 Reorder the terms: -1.5 + t = 12.737739203 Solving -1.5 + t = 12.737739203 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 = 12.737739203 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 12.737739203 + 1.5 t = 12.737739203 + 1.5 Combine like terms: 12.737739203 + 1.5 = 14.237739203 t = 14.237739203 Simplifying t = 14.237739203Subproblem 2
t + -1.5 = -12.737739203 Simplifying t + -1.5 = -12.737739203 Reorder the terms: -1.5 + t = -12.737739203 Solving -1.5 + t = -12.737739203 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 = -12.737739203 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -12.737739203 + 1.5 t = -12.737739203 + 1.5 Combine like terms: -12.737739203 + 1.5 = -11.237739203 t = -11.237739203 Simplifying t = -11.237739203Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.237739203, -11.237739203}
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