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Simplifying -16t2 + 32t + 1760 = 0 Reorder the terms: 1760 + 32t + -16t2 = 0 Solving 1760 + 32t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(110 + 2t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(110 + 2t + -1t2)' equal to zero and attempt to solve: Simplifying 110 + 2t + -1t2 = 0 Solving 110 + 2t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -110 + -2t + t2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + -2t + 110 + t2 = 0 + 110 Reorder the terms: -110 + 110 + -2t + t2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + -2t + t2 = 0 + 110 -2t + t2 = 0 + 110 Combine like terms: 0 + 110 = 110 -2t + t2 = 110 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 = 110 + 1 Reorder the terms: 1 + -2t + t2 = 110 + 1 Combine like terms: 110 + 1 = 111 1 + -2t + t2 = 111 Factor a perfect square on the left side: (t + -1)(t + -1) = 111 Calculate the square root of the right side: 10.535653753 Break this problem into two subproblems by setting (t + -1) equal to 10.535653753 and -10.535653753.Subproblem 1
t + -1 = 10.535653753 Simplifying t + -1 = 10.535653753 Reorder the terms: -1 + t = 10.535653753 Solving -1 + t = 10.535653753 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 = 10.535653753 + 1 Combine like terms: -1 + 1 = 0 0 + t = 10.535653753 + 1 t = 10.535653753 + 1 Combine like terms: 10.535653753 + 1 = 11.535653753 t = 11.535653753 Simplifying t = 11.535653753Subproblem 2
t + -1 = -10.535653753 Simplifying t + -1 = -10.535653753 Reorder the terms: -1 + t = -10.535653753 Solving -1 + t = -10.535653753 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 = -10.535653753 + 1 Combine like terms: -1 + 1 = 0 0 + t = -10.535653753 + 1 t = -10.535653753 + 1 Combine like terms: -10.535653753 + 1 = -9.535653753 t = -9.535653753 Simplifying t = -9.535653753Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.535653753, -9.535653753}Solution
t = {11.535653753, -9.535653753}
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