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Simplifying -5t2 + 50t + 5 = 0 Reorder the terms: 5 + 50t + -5t2 = 0 Solving 5 + 50t + -5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 10t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + 10t + -1t2)' equal to zero and attempt to solve: Simplifying 1 + 10t + -1t2 = 0 Solving 1 + 10t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -10t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -10t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -10t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -10t + t2 = 0 + 1 -10t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -10t + t2 = 1 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 1 + 25 Reorder the terms: 25 + -10t + t2 = 1 + 25 Combine like terms: 1 + 25 = 26 25 + -10t + t2 = 26 Factor a perfect square on the left side: (t + -5)(t + -5) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (t + -5) equal to 5.099019514 and -5.099019514.Subproblem 1
t + -5 = 5.099019514 Simplifying t + -5 = 5.099019514 Reorder the terms: -5 + t = 5.099019514 Solving -5 + t = 5.099019514 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 5.099019514 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.099019514 + 5 t = 5.099019514 + 5 Combine like terms: 5.099019514 + 5 = 10.099019514 t = 10.099019514 Simplifying t = 10.099019514Subproblem 2
t + -5 = -5.099019514 Simplifying t + -5 = -5.099019514 Reorder the terms: -5 + t = -5.099019514 Solving -5 + t = -5.099019514 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -5.099019514 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.099019514 + 5 t = -5.099019514 + 5 Combine like terms: -5.099019514 + 5 = -0.099019514 t = -0.099019514 Simplifying t = -0.099019514Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.099019514, -0.099019514}Solution
t = {10.099019514, -0.099019514}
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