4x^2+11x-29=x+7

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Solution for 4x^2+11x-29=x+7 equation: 


Simplifying
4x2 + 11x + -29 = x + 7

Reorder the terms:
-29 + 11x + 4x2 = x + 7

Reorder the terms:
-29 + 11x + 4x2 = 7 + x

Solving
-29 + 11x + 4x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
-29 + -7 + 11x + -1x + 4x2 = 7 + x + -7 + -1x

Combine like terms: -29 + -7 = -36
-36 + 11x + -1x + 4x2 = 7 + x + -7 + -1x

Combine like terms: 11x + -1x = 10x
-36 + 10x + 4x2 = 7 + x + -7 + -1x

Reorder the terms:
-36 + 10x + 4x2 = 7 + -7 + x + -1x

Combine like terms: 7 + -7 = 0
-36 + 10x + 4x2 = 0 + x + -1x
-36 + 10x + 4x2 = x + -1x

Combine like terms: x + -1x = 0
-36 + 10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 5x + 2x2) = 0

Factor a trinomial.
2((-9 + -2x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4.5, 2}

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