10x-5=x^2+7x+5

Solution for 10x-5=x^2+7x+5 equation:

Simplifying
10x + -5 = x2 + 7x + 5

Reorder the terms:
-5 + 10x = x2 + 7x + 5

Reorder the terms:
-5 + 10x = 5 + 7x + x2

Solving
-5 + 10x = 5 + 7x + x2

Solving for variable 'x'.

Reorder the terms:
-5 + -5 + 10x + -7x + -1x2 = 5 + 7x + x2 + -5 + -7x + -1x2

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

Combine like terms: 10x + -7x = 3x
-10 + 3x + -1x2 = 5 + 7x + x2 + -5 + -7x + -1x2

Reorder the terms:
-10 + 3x + -1x2 = 5 + -5 + 7x + -7x + x2 + -1x2

Combine like terms: 5 + -5 = 0
-10 + 3x + -1x2 = 0 + 7x + -7x + x2 + -1x2
-10 + 3x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
-10 + 3x + -1x2 = 0 + x2 + -1x2
-10 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
10 + -3x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -3x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -3x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x + x2 = 0 + -10
-3x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-3x + x2 = -10

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 = -10 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -10 + 2.25

Combine like terms: -10 + 2.25 = -7.75
2.25 + -3x + x2 = -7.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -7.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.