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Simplifying 176 = -16t2 + 176t Reorder the terms: 176 = 176t + -16t2 Solving 176 = 176t + -16t2 Solving for variable 't'. Reorder the terms: 176 + -176t + 16t2 = 176t + -176t + -16t2 + 16t2 Combine like terms: 176t + -176t = 0 176 + -176t + 16t2 = 0 + -16t2 + 16t2 176 + -176t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 176 + -176t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(11 + -11t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(11 + -11t + t2)' equal to zero and attempt to solve: Simplifying 11 + -11t + t2 = 0 Solving 11 + -11t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -11t + -11 + t2 = 0 + -11 Reorder the terms: 11 + -11 + -11t + t2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -11t + t2 = 0 + -11 -11t + t2 = 0 + -11 Combine like terms: 0 + -11 = -11 -11t + t2 = -11 The t term is -11t. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11t + 30.25 + t2 = -11 + 30.25 Reorder the terms: 30.25 + -11t + t2 = -11 + 30.25 Combine like terms: -11 + 30.25 = 19.25 30.25 + -11t + t2 = 19.25 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (t + -5.5) equal to 4.387482194 and -4.387482194.Subproblem 1
t + -5.5 = 4.387482194 Simplifying t + -5.5 = 4.387482194 Reorder the terms: -5.5 + t = 4.387482194 Solving -5.5 + t = 4.387482194 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = 4.387482194 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = 4.387482194 + 5.5 t = 4.387482194 + 5.5 Combine like terms: 4.387482194 + 5.5 = 9.887482194 t = 9.887482194 Simplifying t = 9.887482194Subproblem 2
t + -5.5 = -4.387482194 Simplifying t + -5.5 = -4.387482194 Reorder the terms: -5.5 + t = -4.387482194 Solving -5.5 + t = -4.387482194 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = -4.387482194 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = -4.387482194 + 5.5 t = -4.387482194 + 5.5 Combine like terms: -4.387482194 + 5.5 = 1.112517806 t = 1.112517806 Simplifying t = 1.112517806Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.887482194, 1.112517806}Solution
t = {9.887482194, 1.112517806}
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