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Simplifying 16t2 + -36t + 12 = 0 Reorder the terms: 12 + -36t + 16t2 = 0 Solving 12 + -36t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -9t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -9t + 4t2)' equal to zero and attempt to solve: Simplifying 3 + -9t + 4t2 = 0 Solving 3 + -9t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -2.25t + t2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -2.25t + -0.75 + t2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -2.25t + t2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -2.25t + t2 = 0 + -0.75 -2.25t + t2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -2.25t + t2 = -0.75 The t term is -2.25t. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25t + 1.265625 + t2 = -0.75 + 1.265625 Reorder the terms: 1.265625 + -2.25t + t2 = -0.75 + 1.265625 Combine like terms: -0.75 + 1.265625 = 0.515625 1.265625 + -2.25t + t2 = 0.515625 Factor a perfect square on the left side: (t + -1.125)(t + -1.125) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (t + -1.125) equal to 0.718070331 and -0.718070331.Subproblem 1
t + -1.125 = 0.718070331 Simplifying t + -1.125 = 0.718070331 Reorder the terms: -1.125 + t = 0.718070331 Solving -1.125 + t = 0.718070331 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = 0.718070331 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = 0.718070331 + 1.125 t = 0.718070331 + 1.125 Combine like terms: 0.718070331 + 1.125 = 1.843070331 t = 1.843070331 Simplifying t = 1.843070331Subproblem 2
t + -1.125 = -0.718070331 Simplifying t + -1.125 = -0.718070331 Reorder the terms: -1.125 + t = -0.718070331 Solving -1.125 + t = -0.718070331 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = -0.718070331 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = -0.718070331 + 1.125 t = -0.718070331 + 1.125 Combine like terms: -0.718070331 + 1.125 = 0.406929669 t = 0.406929669 Simplifying t = 0.406929669Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.843070331, 0.406929669}Solution
t = {1.843070331, 0.406929669}
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