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Simplifying 0 = -4t2 + 4t + 250 Reorder the terms: 0 = 250 + 4t + -4t2 Solving 0 = 250 + 4t + -4t2 Solving for variable 't'. Combine like terms: 0 + -250 = -250 -250 + -4t + 4t2 = 250 + 4t + -4t2 + -250 + -4t + 4t2 Reorder the terms: -250 + -4t + 4t2 = 250 + -250 + 4t + -4t + -4t2 + 4t2 Combine like terms: 250 + -250 = 0 -250 + -4t + 4t2 = 0 + 4t + -4t + -4t2 + 4t2 -250 + -4t + 4t2 = 4t + -4t + -4t2 + 4t2 Combine like terms: 4t + -4t = 0 -250 + -4t + 4t2 = 0 + -4t2 + 4t2 -250 + -4t + 4t2 = -4t2 + 4t2 Combine like terms: -4t2 + 4t2 = 0 -250 + -4t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-125 + -2t + 2t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-125 + -2t + 2t2)' equal to zero and attempt to solve: Simplifying -125 + -2t + 2t2 = 0 Solving -125 + -2t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -62.5 + -1t + t2 = 0 Move the constant term to the right: Add '62.5' to each side of the equation. -62.5 + -1t + 62.5 + t2 = 0 + 62.5 Reorder the terms: -62.5 + 62.5 + -1t + t2 = 0 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + -1t + t2 = 0 + 62.5 -1t + t2 = 0 + 62.5 Combine like terms: 0 + 62.5 = 62.5 -1t + t2 = 62.5 The t term is -1t. 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. -1t + 0.25 + t2 = 62.5 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 62.5 + 0.25 Combine like terms: 62.5 + 0.25 = 62.75 0.25 + -1t + t2 = 62.75 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 62.75 Calculate the square root of the right side: 7.921489759 Break this problem into two subproblems by setting (t + -0.5) equal to 7.921489759 and -7.921489759.Subproblem 1
t + -0.5 = 7.921489759 Simplifying t + -0.5 = 7.921489759 Reorder the terms: -0.5 + t = 7.921489759 Solving -0.5 + t = 7.921489759 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 = 7.921489759 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 7.921489759 + 0.5 t = 7.921489759 + 0.5 Combine like terms: 7.921489759 + 0.5 = 8.421489759 t = 8.421489759 Simplifying t = 8.421489759Subproblem 2
t + -0.5 = -7.921489759 Simplifying t + -0.5 = -7.921489759 Reorder the terms: -0.5 + t = -7.921489759 Solving -0.5 + t = -7.921489759 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 = -7.921489759 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -7.921489759 + 0.5 t = -7.921489759 + 0.5 Combine like terms: -7.921489759 + 0.5 = -7.421489759 t = -7.421489759 Simplifying t = -7.421489759Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.421489759, -7.421489759}Solution
t = {8.421489759, -7.421489759}
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