x^2=10x-31

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Solution for x^2=10x-31 equation:


Simplifying
x2 = 10x + -31

Reorder the terms:
x2 = -31 + 10x

Solving
x2 = -31 + 10x

Solving for variable 'x'.

Reorder the terms:
31 + -10x + x2 = -31 + 10x + 31 + -10x

Reorder the terms:
31 + -10x + x2 = -31 + 31 + 10x + -10x

Combine like terms: -31 + 31 = 0
31 + -10x + x2 = 0 + 10x + -10x
31 + -10x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
31 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + -10x + -31 + x2 = 0 + -31

Reorder the terms:
31 + -31 + -10x + x2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -10x + x2 = 0 + -31
-10x + x2 = 0 + -31

Combine like terms: 0 + -31 = -31
-10x + x2 = -31

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -31 + 25

Reorder the terms:
25 + -10x + x2 = -31 + 25

Combine like terms: -31 + 25 = -6
25 + -10x + x2 = -6

Factor a perfect square on the left side:
(x + -5)(x + -5) = -6

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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