4t^2+9t+1=0

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Solution for 4t^2+9t+1=0 equation:


Simplifying
4t2 + 9t + 1 = 0

Reorder the terms:
1 + 9t + 4t2 = 0

Solving
1 + 9t + 4t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
0.25 + 2.25t + t2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 2.25t + -0.25 + t2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 2.25t + t2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 2.25t + t2 = 0 + -0.25
2.25t + t2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
2.25t + t2 = -0.25

The t term is 2.25t.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25t + 1.265625 + t2 = -0.25 + 1.265625

Reorder the terms:
1.265625 + 2.25t + t2 = -0.25 + 1.265625

Combine like terms: -0.25 + 1.265625 = 1.015625
1.265625 + 2.25t + t2 = 1.015625

Factor a perfect square on the left side:
(t + 1.125)(t + 1.125) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(t + 1.125) equal to 1.007782219 and -1.007782219.

Subproblem 1

t + 1.125 = 1.007782219 Simplifying t + 1.125 = 1.007782219 Reorder the terms: 1.125 + t = 1.007782219 Solving 1.125 + t = 1.007782219 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + t = 1.007782219 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + t = 1.007782219 + -1.125 t = 1.007782219 + -1.125 Combine like terms: 1.007782219 + -1.125 = -0.117217781 t = -0.117217781 Simplifying t = -0.117217781

Subproblem 2

t + 1.125 = -1.007782219 Simplifying t + 1.125 = -1.007782219 Reorder the terms: 1.125 + t = -1.007782219 Solving 1.125 + t = -1.007782219 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + t = -1.007782219 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + t = -1.007782219 + -1.125 t = -1.007782219 + -1.125 Combine like terms: -1.007782219 + -1.125 = -2.132782219 t = -2.132782219 Simplifying t = -2.132782219

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-0.117217781, -2.132782219}

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