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Simplifying 35 + -5t + -5t2 = 0 Solving 35 + -5t + -5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(7 + -1t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(7 + -1t + -1t2)' equal to zero and attempt to solve: Simplifying 7 + -1t + -1t2 = 0 Solving 7 + -1t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + t + t2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + t + 7 + t2 = 0 + 7 Reorder the terms: -7 + 7 + t + t2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + t + t2 = 0 + 7 t + t2 = 0 + 7 Combine like terms: 0 + 7 = 7 t + t2 = 7 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 7 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 7 + 0.25 Combine like terms: 7 + 0.25 = 7.25 1.25 + t2 = 7.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (t + 0.5) equal to 2.692582404 and -2.692582404.Subproblem 1
t + 0.5 = 2.692582404 Simplifying t + 0.5 = 2.692582404 Reorder the terms: 0.5 + t = 2.692582404 Solving 0.5 + t = 2.692582404 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 2.692582404 + -0.5 t = 2.692582404 + -0.5 Combine like terms: 2.692582404 + -0.5 = 2.192582404 t = 2.192582404 Simplifying t = 2.192582404Subproblem 2
t + 0.5 = -2.692582404 Simplifying t + 0.5 = -2.692582404 Reorder the terms: 0.5 + t = -2.692582404 Solving 0.5 + t = -2.692582404 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -2.692582404 + -0.5 t = -2.692582404 + -0.5 Combine like terms: -2.692582404 + -0.5 = -3.192582404 t = -3.192582404 Simplifying t = -3.192582404Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.192582404, -3.192582404}Solution
t = {2.192582404, -3.192582404}
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