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Simplifying 40t2 + 80t + -110 = 0 Reorder the terms: -110 + 80t + 40t2 = 0 Solving -110 + 80t + 40t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '10'. 10(-11 + 8t + 4t2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-11 + 8t + 4t2)' equal to zero and attempt to solve: Simplifying -11 + 8t + 4t2 = 0 Solving -11 + 8t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + 2t + t2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 2t + 2.75 + t2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 2t + t2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 2t + t2 = 0 + 2.75 2t + t2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 2t + t2 = 2.75 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 2.75 + 1 Reorder the terms: 1 + 2t + t2 = 2.75 + 1 Combine like terms: 2.75 + 1 = 3.75 1 + 2t + t2 = 3.75 Factor a perfect square on the left side: (t + 1)(t + 1) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (t + 1) equal to 1.936491673 and -1.936491673.Subproblem 1
t + 1 = 1.936491673 Simplifying t + 1 = 1.936491673 Reorder the terms: 1 + t = 1.936491673 Solving 1 + t = 1.936491673 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 1.936491673 + -1 Combine like terms: 1 + -1 = 0 0 + t = 1.936491673 + -1 t = 1.936491673 + -1 Combine like terms: 1.936491673 + -1 = 0.936491673 t = 0.936491673 Simplifying t = 0.936491673Subproblem 2
t + 1 = -1.936491673 Simplifying t + 1 = -1.936491673 Reorder the terms: 1 + t = -1.936491673 Solving 1 + t = -1.936491673 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -1.936491673 + -1 Combine like terms: 1 + -1 = 0 0 + t = -1.936491673 + -1 t = -1.936491673 + -1 Combine like terms: -1.936491673 + -1 = -2.936491673 t = -2.936491673 Simplifying t = -2.936491673Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.936491673, -2.936491673}Solution
t = {0.936491673, -2.936491673}
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