(x^2)+8x=1

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Solution for (x^2)+8x=1 equation:


Simplifying
(x2) + 8x = 1
x2 + 8x = 1

Reorder the terms:
8x + x2 = 1

Solving
8x + x2 = 1

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 8x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 8x + x2 = 0 + 1

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

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

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 = 1 + 16

Reorder the terms:
16 + 8x + x2 = 1 + 16

Combine like terms: 1 + 16 = 17
16 + 8x + x2 = 17

Factor a perfect square on the left side:
(x + 4)(x + 4) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + 4) equal to 4.123105626 and -4.123105626.

Subproblem 1

x + 4 = 4.123105626 Simplifying x + 4 = 4.123105626 Reorder the terms: 4 + x = 4.123105626 Solving 4 + x = 4.123105626 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 = 4.123105626 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.123105626 + -4 x = 4.123105626 + -4 Combine like terms: 4.123105626 + -4 = 0.123105626 x = 0.123105626 Simplifying x = 0.123105626

Subproblem 2

x + 4 = -4.123105626 Simplifying x + 4 = -4.123105626 Reorder the terms: 4 + x = -4.123105626 Solving 4 + x = -4.123105626 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 = -4.123105626 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.123105626 + -4 x = -4.123105626 + -4 Combine like terms: -4.123105626 + -4 = -8.123105626 x = -8.123105626 Simplifying x = -8.123105626

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.123105626, -8.123105626}

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