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Simplifying 0 = 4t2 + -24t + -25 Reorder the terms: 0 = -25 + -24t + 4t2 Solving 0 = -25 + -24t + 4t2 Solving for variable 't'. Combine like terms: 0 + 25 = 25 25 + 24t + -4t2 = -25 + -24t + 4t2 + 25 + 24t + -4t2 Reorder the terms: 25 + 24t + -4t2 = -25 + 25 + -24t + 24t + 4t2 + -4t2 Combine like terms: -25 + 25 = 0 25 + 24t + -4t2 = 0 + -24t + 24t + 4t2 + -4t2 25 + 24t + -4t2 = -24t + 24t + 4t2 + -4t2 Combine like terms: -24t + 24t = 0 25 + 24t + -4t2 = 0 + 4t2 + -4t2 25 + 24t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 25 + 24t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -6.25 + -6t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -6t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -6t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -6t + t2 = 0 + 6.25 -6t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -6t + t2 = 6.25 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 6.25 + 9 Reorder the terms: 9 + -6t + t2 = 6.25 + 9 Combine like terms: 6.25 + 9 = 15.25 9 + -6t + t2 = 15.25 Factor a perfect square on the left side: (t + -3)(t + -3) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (t + -3) equal to 3.905124838 and -3.905124838.Subproblem 1
t + -3 = 3.905124838 Simplifying t + -3 = 3.905124838 Reorder the terms: -3 + t = 3.905124838 Solving -3 + t = 3.905124838 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 3.905124838 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.905124838 + 3 t = 3.905124838 + 3 Combine like terms: 3.905124838 + 3 = 6.905124838 t = 6.905124838 Simplifying t = 6.905124838Subproblem 2
t + -3 = -3.905124838 Simplifying t + -3 = -3.905124838 Reorder the terms: -3 + t = -3.905124838 Solving -3 + t = -3.905124838 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -3.905124838 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.905124838 + 3 t = -3.905124838 + 3 Combine like terms: -3.905124838 + 3 = -0.905124838 t = -0.905124838 Simplifying t = -0.905124838Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.905124838, -0.905124838}
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