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Simplifying -16t2 + -25t + 200 = 0 Reorder the terms: 200 + -25t + -16t2 = 0 Solving 200 + -25t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -12.5 + 1.5625t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 1.5625t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 1.5625t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 1.5625t + t2 = 0 + 12.5 1.5625t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 1.5625t + t2 = 12.5 The t term is 1.5625t. Take half its coefficient (0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. 1.5625t + 0.6103515625 + t2 = 12.5 + 0.6103515625 Reorder the terms: 0.6103515625 + 1.5625t + t2 = 12.5 + 0.6103515625 Combine like terms: 12.5 + 0.6103515625 = 13.1103515625 0.6103515625 + 1.5625t + t2 = 13.1103515625 Factor a perfect square on the left side: (t + 0.78125)(t + 0.78125) = 13.1103515625 Calculate the square root of the right side: 3.620821946 Break this problem into two subproblems by setting (t + 0.78125) equal to 3.620821946 and -3.620821946.Subproblem 1
t + 0.78125 = 3.620821946 Simplifying t + 0.78125 = 3.620821946 Reorder the terms: 0.78125 + t = 3.620821946 Solving 0.78125 + t = 3.620821946 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + t = 3.620821946 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + t = 3.620821946 + -0.78125 t = 3.620821946 + -0.78125 Combine like terms: 3.620821946 + -0.78125 = 2.839571946 t = 2.839571946 Simplifying t = 2.839571946Subproblem 2
t + 0.78125 = -3.620821946 Simplifying t + 0.78125 = -3.620821946 Reorder the terms: 0.78125 + t = -3.620821946 Solving 0.78125 + t = -3.620821946 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + t = -3.620821946 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + t = -3.620821946 + -0.78125 t = -3.620821946 + -0.78125 Combine like terms: -3.620821946 + -0.78125 = -4.402071946 t = -4.402071946 Simplifying t = -4.402071946Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.839571946, -4.402071946}
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