4x+1=x^2+6x+2

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Solution for 4x+1=x^2+6x+2 equation:


Simplifying
4x + 1 = x2 + 6x + 2

Reorder the terms:
1 + 4x = x2 + 6x + 2

Reorder the terms:
1 + 4x = 2 + 6x + x2

Solving
1 + 4x = 2 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
1 + -2 + 4x + -6x + -1x2 = 2 + 6x + x2 + -2 + -6x + -1x2

Combine like terms: 1 + -2 = -1
-1 + 4x + -6x + -1x2 = 2 + 6x + x2 + -2 + -6x + -1x2

Combine like terms: 4x + -6x = -2x
-1 + -2x + -1x2 = 2 + 6x + x2 + -2 + -6x + -1x2

Reorder the terms:
-1 + -2x + -1x2 = 2 + -2 + 6x + -6x + x2 + -1x2

Combine like terms: 2 + -2 = 0
-1 + -2x + -1x2 = 0 + 6x + -6x + x2 + -1x2
-1 + -2x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-1 + -2x + -1x2 = 0 + x2 + -1x2
-1 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1 + -2x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 2x + x2) = 0

Factor a trinomial.
-1((1 + x)(1 + x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 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 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 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 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-1, -1}

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