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Simplifying 24 + 17t + -35t2 = 0 Solving 24 + 17t + -35t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -35 the coefficient of the squared term: Divide each side by '-35'. -0.6857142857 + -0.4857142857t + t2 = 0 Move the constant term to the right: Add '0.6857142857' to each side of the equation. -0.6857142857 + -0.4857142857t + 0.6857142857 + t2 = 0 + 0.6857142857 Reorder the terms: -0.6857142857 + 0.6857142857 + -0.4857142857t + t2 = 0 + 0.6857142857 Combine like terms: -0.6857142857 + 0.6857142857 = 0.0000000000 0.0000000000 + -0.4857142857t + t2 = 0 + 0.6857142857 -0.4857142857t + t2 = 0 + 0.6857142857 Combine like terms: 0 + 0.6857142857 = 0.6857142857 -0.4857142857t + t2 = 0.6857142857 The t term is -0.4857142857t. Take half its coefficient (-0.2428571429). Square it (0.05897959186) and add it to both sides. Add '0.05897959186' to each side of the equation. -0.4857142857t + 0.05897959186 + t2 = 0.6857142857 + 0.05897959186 Reorder the terms: 0.05897959186 + -0.4857142857t + t2 = 0.6857142857 + 0.05897959186 Combine like terms: 0.6857142857 + 0.05897959186 = 0.74469387756 0.05897959186 + -0.4857142857t + t2 = 0.74469387756 Factor a perfect square on the left side: (t + -0.2428571429)(t + -0.2428571429) = 0.74469387756 Calculate the square root of the right side: 0.862956475 Break this problem into two subproblems by setting (t + -0.2428571429) equal to 0.862956475 and -0.862956475.Subproblem 1
t + -0.2428571429 = 0.862956475 Simplifying t + -0.2428571429 = 0.862956475 Reorder the terms: -0.2428571429 + t = 0.862956475 Solving -0.2428571429 + t = 0.862956475 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2428571429' to each side of the equation. -0.2428571429 + 0.2428571429 + t = 0.862956475 + 0.2428571429 Combine like terms: -0.2428571429 + 0.2428571429 = 0.0000000000 0.0000000000 + t = 0.862956475 + 0.2428571429 t = 0.862956475 + 0.2428571429 Combine like terms: 0.862956475 + 0.2428571429 = 1.1058136179 t = 1.1058136179 Simplifying t = 1.1058136179Subproblem 2
t + -0.2428571429 = -0.862956475 Simplifying t + -0.2428571429 = -0.862956475 Reorder the terms: -0.2428571429 + t = -0.862956475 Solving -0.2428571429 + t = -0.862956475 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2428571429' to each side of the equation. -0.2428571429 + 0.2428571429 + t = -0.862956475 + 0.2428571429 Combine like terms: -0.2428571429 + 0.2428571429 = 0.0000000000 0.0000000000 + t = -0.862956475 + 0.2428571429 t = -0.862956475 + 0.2428571429 Combine like terms: -0.862956475 + 0.2428571429 = -0.6200993321 t = -0.6200993321 Simplifying t = -0.6200993321Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.1058136179, -0.6200993321}
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