4x^2+32x+1=0

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Solution for 4x^2+32x+1=0 equation:


Simplifying
4x2 + 32x + 1 = 0

Reorder the terms:
1 + 32x + 4x2 = 0

Solving
1 + 32x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
0.25 + 8x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 8x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 8x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 8x + x2 = 0 + -0.25
8x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
8x + x2 = -0.25

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -0.25 + 16

Reorder the terms:
16 + 8x + x2 = -0.25 + 16

Combine like terms: -0.25 + 16 = 15.75
16 + 8x + x2 = 15.75

Factor a perfect square on the left side:
(x + 4)(x + 4) = 15.75

Calculate the square root of the right side: 3.968626967

Break this problem into two subproblems by setting 
(x + 4) equal to 3.968626967 and -3.968626967.

Subproblem 1

x + 4 = 3.968626967 Simplifying x + 4 = 3.968626967 Reorder the terms: 4 + x = 3.968626967 Solving 4 + x = 3.968626967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.968626967 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.968626967 + -4 x = 3.968626967 + -4 Combine like terms: 3.968626967 + -4 = -0.031373033 x = -0.031373033 Simplifying x = -0.031373033

Subproblem 2

x + 4 = -3.968626967 Simplifying x + 4 = -3.968626967 Reorder the terms: 4 + x = -3.968626967 Solving 4 + x = -3.968626967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.968626967 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.968626967 + -4 x = -3.968626967 + -4 Combine like terms: -3.968626967 + -4 = -7.968626967 x = -7.968626967 Simplifying x = -7.968626967

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.031373033, -7.968626967}

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