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Simplifying -16t2 + -5t + 4 = -100 Reorder the terms: 4 + -5t + -16t2 = -100 Solving 4 + -5t + -16t2 = -100 Solving for variable 't'. Reorder the terms: 4 + 100 + -5t + -16t2 = -100 + 100 Combine like terms: 4 + 100 = 104 104 + -5t + -16t2 = -100 + 100 Combine like terms: -100 + 100 = 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 = 2.398043261 t = 2.398043261 Simplifying t = 2.398043261Subproblem 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 = -2.710543261 t = -2.710543261 Simplifying t = -2.710543261Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.398043261, -2.710543261}
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