4x^2+8x=1

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Solution for 4x^2+8x=1 equation:


Simplifying
4x2 + 8x = 1

Reorder the terms:
8x + 4x2 = 1

Solving
8x + 4x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 8x + 4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 8x + 4x2 = 0

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

Divide each side by '4'.
-0.25 + 2x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 2x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 2x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 2x + x2 = 0 + 0.25
2x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
2x + x2 = 0.25

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 0.25 + 1

Reorder the terms:
1 + 2x + x2 = 0.25 + 1

Combine like terms: 0.25 + 1 = 1.25
1 + 2x + x2 = 1.25

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 1) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + 1 = 1.118033989 Simplifying x + 1 = 1.118033989 Reorder the terms: 1 + x = 1.118033989 Solving 1 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.118033989 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.118033989 + -1 x = 1.118033989 + -1 Combine like terms: 1.118033989 + -1 = 0.118033989 x = 0.118033989 Simplifying x = 0.118033989

Subproblem 2

x + 1 = -1.118033989 Simplifying x + 1 = -1.118033989 Reorder the terms: 1 + x = -1.118033989 Solving 1 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.118033989 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.118033989 + -1 x = -1.118033989 + -1 Combine like terms: -1.118033989 + -1 = -2.118033989 x = -2.118033989 Simplifying x = -2.118033989

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.118033989, -2.118033989}

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