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Simplifying 10 = 17t + -5t2 Solving 10 = 17t + -5t2 Solving for variable 't'. Reorder the terms: 10 + -17t + 5t2 = 17t + -17t + -5t2 + 5t2 Combine like terms: 17t + -17t = 0 10 + -17t + 5t2 = 0 + -5t2 + 5t2 10 + -17t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 10 + -17t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + -3.4t + t2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.4t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + -3.4t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.4t + t2 = 0 + -2 -3.4t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.4t + t2 = -2 The t term is -3.4t. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4t + 2.89 + t2 = -2 + 2.89 Reorder the terms: 2.89 + -3.4t + t2 = -2 + 2.89 Combine like terms: -2 + 2.89 = 0.89 2.89 + -3.4t + t2 = 0.89 Factor a perfect square on the left side: (t + -1.7)(t + -1.7) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (t + -1.7) equal to 0.943398113 and -0.943398113.Subproblem 1
t + -1.7 = 0.943398113 Simplifying t + -1.7 = 0.943398113 Reorder the terms: -1.7 + t = 0.943398113 Solving -1.7 + t = 0.943398113 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + t = 0.943398113 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + t = 0.943398113 + 1.7 t = 0.943398113 + 1.7 Combine like terms: 0.943398113 + 1.7 = 2.643398113 t = 2.643398113 Simplifying t = 2.643398113Subproblem 2
t + -1.7 = -0.943398113 Simplifying t + -1.7 = -0.943398113 Reorder the terms: -1.7 + t = -0.943398113 Solving -1.7 + t = -0.943398113 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + t = -0.943398113 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + t = -0.943398113 + 1.7 t = -0.943398113 + 1.7 Combine like terms: -0.943398113 + 1.7 = 0.756601887 t = 0.756601887 Simplifying t = 0.756601887Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.643398113, 0.756601887}
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