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Simplifying 4t2 + 16t + 1 = 52 Reorder the terms: 1 + 16t + 4t2 = 52 Solving 1 + 16t + 4t2 = 52 Solving for variable 't'. Reorder the terms: 1 + -52 + 16t + 4t2 = 52 + -52 Combine like terms: 1 + -52 = -51 -51 + 16t + 4t2 = 52 + -52 Combine like terms: 52 + -52 = 0 -51 + 16t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.75 + 4t + t2 = 0 Move the constant term to the right: Add '12.75' to each side of the equation. -12.75 + 4t + 12.75 + t2 = 0 + 12.75 Reorder the terms: -12.75 + 12.75 + 4t + t2 = 0 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + 4t + t2 = 0 + 12.75 4t + t2 = 0 + 12.75 Combine like terms: 0 + 12.75 = 12.75 4t + t2 = 12.75 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = 12.75 + 4 Reorder the terms: 4 + 4t + t2 = 12.75 + 4 Combine like terms: 12.75 + 4 = 16.75 4 + 4t + t2 = 16.75 Factor a perfect square on the left side: (t + 2)(t + 2) = 16.75 Calculate the square root of the right side: 4.092676386 Break this problem into two subproblems by setting (t + 2) equal to 4.092676386 and -4.092676386.Subproblem 1
t + 2 = 4.092676386 Simplifying t + 2 = 4.092676386 Reorder the terms: 2 + t = 4.092676386 Solving 2 + t = 4.092676386 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 4.092676386 + -2 Combine like terms: 2 + -2 = 0 0 + t = 4.092676386 + -2 t = 4.092676386 + -2 Combine like terms: 4.092676386 + -2 = 2.092676386 t = 2.092676386 Simplifying t = 2.092676386Subproblem 2
t + 2 = -4.092676386 Simplifying t + 2 = -4.092676386 Reorder the terms: 2 + t = -4.092676386 Solving 2 + t = -4.092676386 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = -4.092676386 + -2 Combine like terms: 2 + -2 = 0 0 + t = -4.092676386 + -2 t = -4.092676386 + -2 Combine like terms: -4.092676386 + -2 = -6.092676386 t = -6.092676386 Simplifying t = -6.092676386Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.092676386, -6.092676386}
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