a+(a-1)+2x(a+1)=49

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Solution for a+(a-1)+2x(a+1)=49 equation:


Simplifying
a + (a + -1) + 2x(a + 1) = 49

Reorder the terms:
a + (-1 + a) + 2x(a + 1) = 49

Remove parenthesis around (-1 + a)
a + -1 + a + 2x(a + 1) = 49

Reorder the terms:
a + -1 + a + 2x(1 + a) = 49
a + -1 + a + (1 * 2x + a * 2x) = 49

Reorder the terms:
a + -1 + a + (2ax + 2x) = 49
a + -1 + a + (2ax + 2x) = 49

Reorder the terms:
-1 + a + a + 2ax + 2x = 49

Combine like terms: a + a = 2a
-1 + 2a + 2ax + 2x = 49

Solving
-1 + 2a + 2ax + 2x = 49

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 2a + 2ax + 1 + 2x = 49 + 1

Reorder the terms:
-1 + 1 + 2a + 2ax + 2x = 49 + 1

Combine like terms: -1 + 1 = 0
0 + 2a + 2ax + 2x = 49 + 1
2a + 2ax + 2x = 49 + 1

Combine like terms: 49 + 1 = 50
2a + 2ax + 2x = 50

Add '-2x' to each side of the equation.
2a + 2ax + 2x + -2x = 50 + -2x

Combine like terms: 2x + -2x = 0
2a + 2ax + 0 = 50 + -2x
2a + 2ax = 50 + -2x

Reorder the terms:
-50 + 2a + 2ax + 2x = 50 + -2x + -50 + 2x

Reorder the terms:
-50 + 2a + 2ax + 2x = 50 + -50 + -2x + 2x

Combine like terms: 50 + -50 = 0
-50 + 2a + 2ax + 2x = 0 + -2x + 2x
-50 + 2a + 2ax + 2x = -2x + 2x

Combine like terms: -2x + 2x = 0
-50 + 2a + 2ax + 2x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + a + ax + x) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-25 + a + ax + x)' equal to zero and attempt to solve: Simplifying -25 + a + ax + x = 0 Solving -25 + a + ax + x = 0 Move all terms containing a to the left, all other terms to the right. Add '25' to each side of the equation. -25 + a + ax + 25 + x = 0 + 25 Reorder the terms: -25 + 25 + a + ax + x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + a + ax + x = 0 + 25 a + ax + x = 0 + 25 Combine like terms: 0 + 25 = 25 a + ax + x = 25 Add '-1x' to each side of the equation. a + ax + x + -1x = 25 + -1x Combine like terms: x + -1x = 0 a + ax + 0 = 25 + -1x a + ax = 25 + -1x 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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