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Simplifying -100 = -16t2 + 5t + 4 Reorder the terms: -100 = 4 + 5t + -16t2 Solving -100 = 4 + 5t + -16t2 Solving for variable 't'. Combine like terms: -100 + -4 = -104 -104 + -5t + 16t2 = 4 + 5t + -16t2 + -4 + -5t + 16t2 Reorder the terms: -104 + -5t + 16t2 = 4 + -4 + 5t + -5t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 -104 + -5t + 16t2 = 0 + 5t + -5t + -16t2 + 16t2 -104 + -5t + 16t2 = 5t + -5t + -16t2 + 16t2 Combine like terms: 5t + -5t = 0 -104 + -5t + 16t2 = 0 + -16t2 + 16t2 -104 + -5t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -104 + -5t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -6.5 + -0.3125t + t2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -0.3125t + 6.5 + t2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -0.3125t + t2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -0.3125t + t2 = 0 + 6.5 -0.3125t + t2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -0.3125t + t2 = 6.5 The t term is -0.3125t. Take half its coefficient (-0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. -0.3125t + 0.0244140625 + t2 = 6.5 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125t + t2 = 6.5 + 0.0244140625 Combine like terms: 6.5 + 0.0244140625 = 6.5244140625 0.0244140625 + -0.3125t + t2 = 6.5244140625 Factor a perfect square on the left side: (t + -0.15625)(t + -0.15625) = 6.5244140625 Calculate the square root of the right side: 2.554293261 Break this problem into two subproblems by setting (t + -0.15625) equal to 2.554293261 and -2.554293261.Subproblem 1
t + -0.15625 = 2.554293261 Simplifying t + -0.15625 = 2.554293261 Reorder the terms: -0.15625 + t = 2.554293261 Solving -0.15625 + t = 2.554293261 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = 2.554293261 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = 2.554293261 + 0.15625 t = 2.554293261 + 0.15625 Combine like terms: 2.554293261 + 0.15625 = 2.710543261 t = 2.710543261 Simplifying t = 2.710543261Subproblem 2
t + -0.15625 = -2.554293261 Simplifying t + -0.15625 = -2.554293261 Reorder the terms: -0.15625 + t = -2.554293261 Solving -0.15625 + t = -2.554293261 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = -2.554293261 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = -2.554293261 + 0.15625 t = -2.554293261 + 0.15625 Combine like terms: -2.554293261 + 0.15625 = -2.398043261 t = -2.398043261 Simplifying t = -2.398043261Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.710543261, -2.398043261}
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