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Simplifying 6 + 48t + -16t2 = 0 Solving 6 + 48t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 24t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 24t + -8t2)' equal to zero and attempt to solve: Simplifying 3 + 24t + -8t2 = 0 Solving 3 + 24t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -3t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -3t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -3t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -3t + t2 = 0 + 0.375 -3t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -3t + t2 = 0.375 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 = 0.375 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 0.375 + 2.25 Combine like terms: 0.375 + 2.25 = 2.625 2.25 + -3t + t2 = 2.625 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 2.625 Calculate the square root of the right side: 1.620185175 Break this problem into two subproblems by setting (t + -1.5) equal to 1.620185175 and -1.620185175.Subproblem 1
t + -1.5 = 1.620185175 Simplifying t + -1.5 = 1.620185175 Reorder the terms: -1.5 + t = 1.620185175 Solving -1.5 + t = 1.620185175 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 = 1.620185175 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 1.620185175 + 1.5 t = 1.620185175 + 1.5 Combine like terms: 1.620185175 + 1.5 = 3.120185175 t = 3.120185175 Simplifying t = 3.120185175Subproblem 2
t + -1.5 = -1.620185175 Simplifying t + -1.5 = -1.620185175 Reorder the terms: -1.5 + t = -1.620185175 Solving -1.5 + t = -1.620185175 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 = -1.620185175 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -1.620185175 + 1.5 t = -1.620185175 + 1.5 Combine like terms: -1.620185175 + 1.5 = -0.120185175 t = -0.120185175 Simplifying t = -0.120185175Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.120185175, -0.120185175}Solution
t = {3.120185175, -0.120185175}
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