2x(5+x)-2=6(x-2)+2x

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Solution for 2x(5+x)-2=6(x-2)+2x equation:


Simplifying
2x(5 + x) + -2 = 6(x + -2) + 2x
(5 * 2x + x * 2x) + -2 = 6(x + -2) + 2x
(10x + 2x2) + -2 = 6(x + -2) + 2x

Reorder the terms:
-2 + 10x + 2x2 = 6(x + -2) + 2x

Reorder the terms:
-2 + 10x + 2x2 = 6(-2 + x) + 2x
-2 + 10x + 2x2 = (-2 * 6 + x * 6) + 2x
-2 + 10x + 2x2 = (-12 + 6x) + 2x

Combine like terms: 6x + 2x = 8x
-2 + 10x + 2x2 = -12 + 8x

Solving
-2 + 10x + 2x2 = -12 + 8x

Solving for variable 'x'.

Reorder the terms:
-2 + 12 + 10x + -8x + 2x2 = -12 + 8x + 12 + -8x

Combine like terms: -2 + 12 = 10
10 + 10x + -8x + 2x2 = -12 + 8x + 12 + -8x

Combine like terms: 10x + -8x = 2x
10 + 2x + 2x2 = -12 + 8x + 12 + -8x

Reorder the terms:
10 + 2x + 2x2 = -12 + 12 + 8x + -8x

Combine like terms: -12 + 12 = 0
10 + 2x + 2x2 = 0 + 8x + -8x
10 + 2x + 2x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
10 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + x + x2)' equal to zero and attempt to solve: Simplifying 5 + x + x2 = 0 Solving 5 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x + x2 = 0 + -5 x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 x + x2 = -5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = -5 + 0.25 Reorder the terms: 0.25 + x + x2 = -5 + 0.25 Combine like terms: -5 + 0.25 = -4.75 0.25 + x + x2 = -4.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -4.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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