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Simplifying -16t2 + 60t + 400 = 0 Reorder the terms: 400 + 60t + -16t2 = 0 Solving 400 + 60t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(100 + 15t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(100 + 15t + -4t2)' equal to zero and attempt to solve: Simplifying 100 + 15t + -4t2 = 0 Solving 100 + 15t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -25 + -3.75t + t2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -3.75t + 25 + t2 = 0 + 25 Reorder the terms: -25 + 25 + -3.75t + t2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -3.75t + t2 = 0 + 25 -3.75t + t2 = 0 + 25 Combine like terms: 0 + 25 = 25 -3.75t + t2 = 25 The t term is -3.75t. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75t + 3.515625 + t2 = 25 + 3.515625 Reorder the terms: 3.515625 + -3.75t + t2 = 25 + 3.515625 Combine like terms: 25 + 3.515625 = 28.515625 3.515625 + -3.75t + t2 = 28.515625 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = 28.515625 Calculate the square root of the right side: 5.340002341 Break this problem into two subproblems by setting (t + -1.875) equal to 5.340002341 and -5.340002341.Subproblem 1
t + -1.875 = 5.340002341 Simplifying t + -1.875 = 5.340002341 Reorder the terms: -1.875 + t = 5.340002341 Solving -1.875 + t = 5.340002341 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = 5.340002341 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 5.340002341 + 1.875 t = 5.340002341 + 1.875 Combine like terms: 5.340002341 + 1.875 = 7.215002341 t = 7.215002341 Simplifying t = 7.215002341Subproblem 2
t + -1.875 = -5.340002341 Simplifying t + -1.875 = -5.340002341 Reorder the terms: -1.875 + t = -5.340002341 Solving -1.875 + t = -5.340002341 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = -5.340002341 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -5.340002341 + 1.875 t = -5.340002341 + 1.875 Combine like terms: -5.340002341 + 1.875 = -3.465002341 t = -3.465002341 Simplifying t = -3.465002341Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.215002341, -3.465002341}Solution
t = {7.215002341, -3.465002341}
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