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Simplifying 25(t) = -16t2 + 25 Reorder the terms: 25t = 25 + -16t2 Solving 25t = 25 + -16t2 Solving for variable 't'. Reorder the terms: -25 + 25t + 16t2 = 25 + -16t2 + -25 + 16t2 Reorder the terms: -25 + 25t + 16t2 = 25 + -25 + -16t2 + 16t2 Combine like terms: 25 + -25 = 0 -25 + 25t + 16t2 = 0 + -16t2 + 16t2 -25 + 25t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -25 + 25t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + 1.5625t + t2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + 1.5625t + 1.5625 + t2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + 1.5625t + t2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + 1.5625t + t2 = 0 + 1.5625 1.5625t + t2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 1.5625t + t2 = 1.5625 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 = 1.5625 + 0.6103515625 Reorder the terms: 0.6103515625 + 1.5625t + t2 = 1.5625 + 0.6103515625 Combine like terms: 1.5625 + 0.6103515625 = 2.1728515625 0.6103515625 + 1.5625t + t2 = 2.1728515625 Factor a perfect square on the left side: (t + 0.78125)(t + 0.78125) = 2.1728515625 Calculate the square root of the right side: 1.474059552 Break this problem into two subproblems by setting (t + 0.78125) equal to 1.474059552 and -1.474059552.Subproblem 1
t + 0.78125 = 1.474059552 Simplifying t + 0.78125 = 1.474059552 Reorder the terms: 0.78125 + t = 1.474059552 Solving 0.78125 + t = 1.474059552 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 = 1.474059552 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + t = 1.474059552 + -0.78125 t = 1.474059552 + -0.78125 Combine like terms: 1.474059552 + -0.78125 = 0.692809552 t = 0.692809552 Simplifying t = 0.692809552Subproblem 2
t + 0.78125 = -1.474059552 Simplifying t + 0.78125 = -1.474059552 Reorder the terms: 0.78125 + t = -1.474059552 Solving 0.78125 + t = -1.474059552 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 = -1.474059552 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + t = -1.474059552 + -0.78125 t = -1.474059552 + -0.78125 Combine like terms: -1.474059552 + -0.78125 = -2.255309552 t = -2.255309552 Simplifying t = -2.255309552Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.692809552, -2.255309552}
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