4t^2+16t+1=52

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Solution for 4t^2+16t+1=52 equation:


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 = 2.092676386

Subproblem 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 = -6.092676386

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.092676386, -6.092676386}

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