2x^2+19=6x+7

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Solution for 2x^2+19=6x+7 equation: 


Simplifying
2x2 + 19 = 6x + 7

Reorder the terms:
19 + 2x2 = 6x + 7

Reorder the terms:
19 + 2x2 = 7 + 6x

Solving
19 + 2x2 = 7 + 6x

Solving for variable 'x'.

Reorder the terms:
19 + -7 + -6x + 2x2 = 7 + 6x + -7 + -6x

Combine like terms: 19 + -7 = 12
12 + -6x + 2x2 = 7 + 6x + -7 + -6x

Reorder the terms:
12 + -6x + 2x2 = 7 + -7 + 6x + -6x

Combine like terms: 7 + -7 = 0
12 + -6x + 2x2 = 0 + 6x + -6x
12 + -6x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
12 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(6 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
6 + -3x + x2 = 0

Solving
6 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -3x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -3x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -3x + x2 = 0 + -6
-3x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-3x + x2 = -6

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -6 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -6 + 2.25

Combine like terms: -6 + 2.25 = -3.75
2.25 + -3x + x2 = -3.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -3.75

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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