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Simplifying -16t2 + 88t + 4 = 0 Reorder the terms: 4 + 88t + -16t2 = 0 Solving 4 + 88t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 22t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 22t + -4t2)' equal to zero and attempt to solve: Simplifying 1 + 22t + -4t2 = 0 Solving 1 + 22t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -5.5t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -5.5t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -5.5t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -5.5t + t2 = 0 + 0.25 -5.5t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -5.5t + t2 = 0.25 The t term is -5.5t. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5t + 7.5625 + t2 = 0.25 + 7.5625 Reorder the terms: 7.5625 + -5.5t + t2 = 0.25 + 7.5625 Combine like terms: 0.25 + 7.5625 = 7.8125 7.5625 + -5.5t + t2 = 7.8125 Factor a perfect square on the left side: (t + -2.75)(t + -2.75) = 7.8125 Calculate the square root of the right side: 2.795084972 Break this problem into two subproblems by setting (t + -2.75) equal to 2.795084972 and -2.795084972.Subproblem 1
t + -2.75 = 2.795084972 Simplifying t + -2.75 = 2.795084972 Reorder the terms: -2.75 + t = 2.795084972 Solving -2.75 + t = 2.795084972 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t = 2.795084972 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = 2.795084972 + 2.75 t = 2.795084972 + 2.75 Combine like terms: 2.795084972 + 2.75 = 5.545084972 t = 5.545084972 Simplifying t = 5.545084972Subproblem 2
t + -2.75 = -2.795084972 Simplifying t + -2.75 = -2.795084972 Reorder the terms: -2.75 + t = -2.795084972 Solving -2.75 + t = -2.795084972 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t = -2.795084972 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = -2.795084972 + 2.75 t = -2.795084972 + 2.75 Combine like terms: -2.795084972 + 2.75 = -0.045084972 t = -0.045084972 Simplifying t = -0.045084972Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.545084972, -0.045084972}Solution
t = {5.545084972, -0.045084972}
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