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Simplifying 16t2 + -164t + -36 = 0 Reorder the terms: -36 + -164t + 16t2 = 0 Solving -36 + -164t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + -41t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -41t + 4t2)' equal to zero and attempt to solve: Simplifying -9 + -41t + 4t2 = 0 Solving -9 + -41t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -10.25t + t2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -10.25t + 2.25 + t2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -10.25t + t2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -10.25t + t2 = 0 + 2.25 -10.25t + t2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -10.25t + t2 = 2.25 The t term is -10.25t. Take half its coefficient (-5.125). Square it (26.265625) and add it to both sides. Add '26.265625' to each side of the equation. -10.25t + 26.265625 + t2 = 2.25 + 26.265625 Reorder the terms: 26.265625 + -10.25t + t2 = 2.25 + 26.265625 Combine like terms: 2.25 + 26.265625 = 28.515625 26.265625 + -10.25t + t2 = 28.515625 Factor a perfect square on the left side: (t + -5.125)(t + -5.125) = 28.515625 Calculate the square root of the right side: 5.340002341 Break this problem into two subproblems by setting (t + -5.125) equal to 5.340002341 and -5.340002341.Subproblem 1
t + -5.125 = 5.340002341 Simplifying t + -5.125 = 5.340002341 Reorder the terms: -5.125 + t = 5.340002341 Solving -5.125 + t = 5.340002341 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + t = 5.340002341 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + t = 5.340002341 + 5.125 t = 5.340002341 + 5.125 Combine like terms: 5.340002341 + 5.125 = 10.465002341 t = 10.465002341 Simplifying t = 10.465002341Subproblem 2
t + -5.125 = -5.340002341 Simplifying t + -5.125 = -5.340002341 Reorder the terms: -5.125 + t = -5.340002341 Solving -5.125 + t = -5.340002341 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + t = -5.340002341 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + t = -5.340002341 + 5.125 t = -5.340002341 + 5.125 Combine like terms: -5.340002341 + 5.125 = -0.215002341 t = -0.215002341 Simplifying t = -0.215002341Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.465002341, -0.215002341}Solution
t = {10.465002341, -0.215002341}
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