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Simplifying 4t2 + 20t + -14 = 0 Reorder the terms: -14 + 20t + 4t2 = 0 Solving -14 + 20t + 4t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 10t + 2t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 10t + 2t2)' equal to zero and attempt to solve: Simplifying -7 + 10t + 2t2 = 0 Solving -7 + 10t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 5t + t2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 5t + 3.5 + t2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 5t + t2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 5t + t2 = 0 + 3.5 5t + t2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 5t + t2 = 3.5 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = 3.5 + 6.25 Reorder the terms: 6.25 + 5t + t2 = 3.5 + 6.25 Combine like terms: 3.5 + 6.25 = 9.75 6.25 + 5t + t2 = 9.75 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = 9.75 Calculate the square root of the right side: 3.122498999 Break this problem into two subproblems by setting (t + 2.5) equal to 3.122498999 and -3.122498999.Subproblem 1
t + 2.5 = 3.122498999 Simplifying t + 2.5 = 3.122498999 Reorder the terms: 2.5 + t = 3.122498999 Solving 2.5 + t = 3.122498999 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = 3.122498999 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 3.122498999 + -2.5 t = 3.122498999 + -2.5 Combine like terms: 3.122498999 + -2.5 = 0.622498999 t = 0.622498999 Simplifying t = 0.622498999Subproblem 2
t + 2.5 = -3.122498999 Simplifying t + 2.5 = -3.122498999 Reorder the terms: 2.5 + t = -3.122498999 Solving 2.5 + t = -3.122498999 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = -3.122498999 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -3.122498999 + -2.5 t = -3.122498999 + -2.5 Combine like terms: -3.122498999 + -2.5 = -5.622498999 t = -5.622498999 Simplifying t = -5.622498999Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.622498999, -5.622498999}Solution
t = {0.622498999, -5.622498999}
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