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Simplifying 0 = -16t2 + 72t + 20 Reorder the terms: 0 = 20 + 72t + -16t2 Solving 0 = 20 + 72t + -16t2 Solving for variable 't'. Combine like terms: 0 + -20 = -20 -20 + -72t + 16t2 = 20 + 72t + -16t2 + -20 + -72t + 16t2 Reorder the terms: -20 + -72t + 16t2 = 20 + -20 + 72t + -72t + -16t2 + 16t2 Combine like terms: 20 + -20 = 0 -20 + -72t + 16t2 = 0 + 72t + -72t + -16t2 + 16t2 -20 + -72t + 16t2 = 72t + -72t + -16t2 + 16t2 Combine like terms: 72t + -72t = 0 -20 + -72t + 16t2 = 0 + -16t2 + 16t2 -20 + -72t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -20 + -72t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -18t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -18t + 4t2)' equal to zero and attempt to solve: Simplifying -5 + -18t + 4t2 = 0 Solving -5 + -18t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -4.5t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -4.5t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -4.5t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -4.5t + t2 = 0 + 1.25 -4.5t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -4.5t + t2 = 1.25 The t term is -4.5t. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5t + 5.0625 + t2 = 1.25 + 5.0625 Reorder the terms: 5.0625 + -4.5t + t2 = 1.25 + 5.0625 Combine like terms: 1.25 + 5.0625 = 6.3125 5.0625 + -4.5t + t2 = 6.3125 Factor a perfect square on the left side: (t + -2.25)(t + -2.25) = 6.3125 Calculate the square root of the right side: 2.512468905 Break this problem into two subproblems by setting (t + -2.25) equal to 2.512468905 and -2.512468905.Subproblem 1
t + -2.25 = 2.512468905 Simplifying t + -2.25 = 2.512468905 Reorder the terms: -2.25 + t = 2.512468905 Solving -2.25 + t = 2.512468905 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = 2.512468905 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = 2.512468905 + 2.25 t = 2.512468905 + 2.25 Combine like terms: 2.512468905 + 2.25 = 4.762468905 t = 4.762468905 Simplifying t = 4.762468905Subproblem 2
t + -2.25 = -2.512468905 Simplifying t + -2.25 = -2.512468905 Reorder the terms: -2.25 + t = -2.512468905 Solving -2.25 + t = -2.512468905 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = -2.512468905 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = -2.512468905 + 2.25 t = -2.512468905 + 2.25 Combine like terms: -2.512468905 + 2.25 = -0.262468905 t = -0.262468905 Simplifying t = -0.262468905Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.762468905, -0.262468905}Solution
t = {4.762468905, -0.262468905}
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