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Simplifying -16t2 + 80t + 60 = 0 Reorder the terms: 60 + 80t + -16t2 = 0 Solving 60 + 80t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(15 + 20t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(15 + 20t + -4t2)' equal to zero and attempt to solve: Simplifying 15 + 20t + -4t2 = 0 Solving 15 + 20t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3.75 + -5t + t2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -5t + 3.75 + t2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -5t + t2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -5t + t2 = 0 + 3.75 -5t + t2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -5t + t2 = 3.75 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 3.75 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 3.75 + 6.25 Combine like terms: 3.75 + 6.25 = 10 6.25 + -5t + t2 = 10 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (t + -2.5) equal to 3.16227766 and -3.16227766.Subproblem 1
t + -2.5 = 3.16227766 Simplifying t + -2.5 = 3.16227766 Reorder the terms: -2.5 + t = 3.16227766 Solving -2.5 + t = 3.16227766 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 3.16227766 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 3.16227766 + 2.5 t = 3.16227766 + 2.5 Combine like terms: 3.16227766 + 2.5 = 5.66227766 t = 5.66227766 Simplifying t = 5.66227766Subproblem 2
t + -2.5 = -3.16227766 Simplifying t + -2.5 = -3.16227766 Reorder the terms: -2.5 + t = -3.16227766 Solving -2.5 + t = -3.16227766 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -3.16227766 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -3.16227766 + 2.5 t = -3.16227766 + 2.5 Combine like terms: -3.16227766 + 2.5 = -0.66227766 t = -0.66227766 Simplifying t = -0.66227766Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.66227766, -0.66227766}Solution
t = {5.66227766, -0.66227766}
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