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Simplifying -16t2 + 48t + 196 = 0 Reorder the terms: 196 + 48t + -16t2 = 0 Solving 196 + 48t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(49 + 12t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(49 + 12t + -4t2)' equal to zero and attempt to solve: Simplifying 49 + 12t + -4t2 = 0 Solving 49 + 12t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -12.25 + -3t + t2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + -3t + 12.25 + t2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + -3t + t2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + -3t + t2 = 0 + 12.25 -3t + t2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 -3t + t2 = 12.25 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = 12.25 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 12.25 + 2.25 Combine like terms: 12.25 + 2.25 = 14.5 2.25 + -3t + t2 = 14.5 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (t + -1.5) equal to 3.807886553 and -3.807886553.Subproblem 1
t + -1.5 = 3.807886553 Simplifying t + -1.5 = 3.807886553 Reorder the terms: -1.5 + t = 3.807886553 Solving -1.5 + t = 3.807886553 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 3.807886553 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 3.807886553 + 1.5 t = 3.807886553 + 1.5 Combine like terms: 3.807886553 + 1.5 = 5.307886553 t = 5.307886553 Simplifying t = 5.307886553Subproblem 2
t + -1.5 = -3.807886553 Simplifying t + -1.5 = -3.807886553 Reorder the terms: -1.5 + t = -3.807886553 Solving -1.5 + t = -3.807886553 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -3.807886553 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -3.807886553 + 1.5 t = -3.807886553 + 1.5 Combine like terms: -3.807886553 + 1.5 = -2.307886553 t = -2.307886553 Simplifying t = -2.307886553Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.307886553, -2.307886553}Solution
t = {5.307886553, -2.307886553}
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