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Simplifying 20 = -16t2 + 170t + 50 Reorder the terms: 20 = 50 + 170t + -16t2 Solving 20 = 50 + 170t + -16t2 Solving for variable 't'. Combine like terms: 20 + -50 = -30 -30 + -170t + 16t2 = 50 + 170t + -16t2 + -50 + -170t + 16t2 Reorder the terms: -30 + -170t + 16t2 = 50 + -50 + 170t + -170t + -16t2 + 16t2 Combine like terms: 50 + -50 = 0 -30 + -170t + 16t2 = 0 + 170t + -170t + -16t2 + 16t2 -30 + -170t + 16t2 = 170t + -170t + -16t2 + 16t2 Combine like terms: 170t + -170t = 0 -30 + -170t + 16t2 = 0 + -16t2 + 16t2 -30 + -170t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -30 + -170t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -85t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -85t + 8t2)' equal to zero and attempt to solve: Simplifying -15 + -85t + 8t2 = 0 Solving -15 + -85t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + -10.625t + t2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -10.625t + 1.875 + t2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -10.625t + t2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -10.625t + t2 = 0 + 1.875 -10.625t + t2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -10.625t + t2 = 1.875 The t term is -10.625t. Take half its coefficient (-5.3125). Square it (28.22265625) and add it to both sides. Add '28.22265625' to each side of the equation. -10.625t + 28.22265625 + t2 = 1.875 + 28.22265625 Reorder the terms: 28.22265625 + -10.625t + t2 = 1.875 + 28.22265625 Combine like terms: 1.875 + 28.22265625 = 30.09765625 28.22265625 + -10.625t + t2 = 30.09765625 Factor a perfect square on the left side: (t + -5.3125)(t + -5.3125) = 30.09765625 Calculate the square root of the right side: 5.486133087 Break this problem into two subproblems by setting (t + -5.3125) equal to 5.486133087 and -5.486133087.Subproblem 1
t + -5.3125 = 5.486133087 Simplifying t + -5.3125 = 5.486133087 Reorder the terms: -5.3125 + t = 5.486133087 Solving -5.3125 + t = 5.486133087 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.3125' to each side of the equation. -5.3125 + 5.3125 + t = 5.486133087 + 5.3125 Combine like terms: -5.3125 + 5.3125 = 0.0000 0.0000 + t = 5.486133087 + 5.3125 t = 5.486133087 + 5.3125 Combine like terms: 5.486133087 + 5.3125 = 10.798633087 t = 10.798633087 Simplifying t = 10.798633087Subproblem 2
t + -5.3125 = -5.486133087 Simplifying t + -5.3125 = -5.486133087 Reorder the terms: -5.3125 + t = -5.486133087 Solving -5.3125 + t = -5.486133087 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.3125' to each side of the equation. -5.3125 + 5.3125 + t = -5.486133087 + 5.3125 Combine like terms: -5.3125 + 5.3125 = 0.0000 0.0000 + t = -5.486133087 + 5.3125 t = -5.486133087 + 5.3125 Combine like terms: -5.486133087 + 5.3125 = -0.173633087 t = -0.173633087 Simplifying t = -0.173633087Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.798633087, -0.173633087}Solution
t = {10.798633087, -0.173633087}
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