5x^2+6x+7=x^2-4x

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Solution for 5x^2+6x+7=x^2-4x equation: 


Simplifying
5x2 + 6x + 7 = x2 + -4x

Reorder the terms:
7 + 6x + 5x2 = x2 + -4x

Reorder the terms:
7 + 6x + 5x2 = -4x + x2

Solving
7 + 6x + 5x2 = -4x + x2

Solving for variable 'x'.

Reorder the terms:
7 + 6x + 4x + 5x2 + -1x2 = -4x + x2 + 4x + -1x2

Combine like terms: 6x + 4x = 10x
7 + 10x + 5x2 + -1x2 = -4x + x2 + 4x + -1x2

Combine like terms: 5x2 + -1x2 = 4x2
7 + 10x + 4x2 = -4x + x2 + 4x + -1x2

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

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

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

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

Divide each side by '4'.
1.75 + 2.5x + x2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + 2.5x + -1.75 + x2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + 2.5x + x2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + 2.5x + x2 = 0 + -1.75
2.5x + x2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
2.5x + x2 = -1.75

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = -1.75 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = -1.75 + 1.5625

Combine like terms: -1.75 + 1.5625 = -0.1875
1.5625 + 2.5x + x2 = -0.1875

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = -0.1875

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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