4x^2+10x+6=6x^2+19

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Solution for 4x^2+10x+6=6x^2+19 equation:


Simplifying
4x2 + 10x + 6 = 6x2 + 19

Reorder the terms:
6 + 10x + 4x2 = 6x2 + 19

Reorder the terms:
6 + 10x + 4x2 = 19 + 6x2

Solving
6 + 10x + 4x2 = 19 + 6x2

Solving for variable 'x'.

Reorder the terms:
6 + -19 + 10x + 4x2 + -6x2 = 19 + 6x2 + -19 + -6x2

Combine like terms: 6 + -19 = -13
-13 + 10x + 4x2 + -6x2 = 19 + 6x2 + -19 + -6x2

Combine like terms: 4x2 + -6x2 = -2x2
-13 + 10x + -2x2 = 19 + 6x2 + -19 + -6x2

Reorder the terms:
-13 + 10x + -2x2 = 19 + -19 + 6x2 + -6x2

Combine like terms: 19 + -19 = 0
-13 + 10x + -2x2 = 0 + 6x2 + -6x2
-13 + 10x + -2x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-13 + 10x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
6.5 + -5x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + -5x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + -5x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + -5x + x2 = 0 + -6.5
-5x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
-5x + x2 = -6.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -6.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -6.5 + 6.25

Combine like terms: -6.5 + 6.25 = -0.25
6.25 + -5x + x2 = -0.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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