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Simplifying -16t2 + 48t + 8 = 0 Reorder the terms: 8 + 48t + -16t2 = 0 Solving 8 + 48t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(1 + 6t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + 6t + -2t2)' equal to zero and attempt to solve: Simplifying 1 + 6t + -2t2 = 0 Solving 1 + 6t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -3t + t2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -3t + 0.5 + t2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -3t + t2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -3t + t2 = 0 + 0.5 -3t + t2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -3t + t2 = 0.5 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 = 0.5 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 0.5 + 2.25 Combine like terms: 0.5 + 2.25 = 2.75 2.25 + -3t + t2 = 2.75 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (t + -1.5) equal to 1.658312395 and -1.658312395.Subproblem 1
t + -1.5 = 1.658312395 Simplifying t + -1.5 = 1.658312395 Reorder the terms: -1.5 + t = 1.658312395 Solving -1.5 + t = 1.658312395 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 = 1.658312395 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 1.658312395 + 1.5 t = 1.658312395 + 1.5 Combine like terms: 1.658312395 + 1.5 = 3.158312395 t = 3.158312395 Simplifying t = 3.158312395Subproblem 2
t + -1.5 = -1.658312395 Simplifying t + -1.5 = -1.658312395 Reorder the terms: -1.5 + t = -1.658312395 Solving -1.5 + t = -1.658312395 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 = -1.658312395 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -1.658312395 + 1.5 t = -1.658312395 + 1.5 Combine like terms: -1.658312395 + 1.5 = -0.158312395 t = -0.158312395 Simplifying t = -0.158312395Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.158312395, -0.158312395}Solution
t = {3.158312395, -0.158312395}
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