-x+10=x^2-5x+15

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Solution for -x+10=x^2-5x+15 equation:


Simplifying
-1x + 10 = x2 + -5x + 15

Reorder the terms:
10 + -1x = x2 + -5x + 15

Reorder the terms:
10 + -1x = 15 + -5x + x2

Solving
10 + -1x = 15 + -5x + x2

Solving for variable 'x'.

Reorder the terms:
10 + -15 + -1x + 5x + -1x2 = 15 + -5x + x2 + -15 + 5x + -1x2

Combine like terms: 10 + -15 = -5
-5 + -1x + 5x + -1x2 = 15 + -5x + x2 + -15 + 5x + -1x2

Combine like terms: -1x + 5x = 4x
-5 + 4x + -1x2 = 15 + -5x + x2 + -15 + 5x + -1x2

Reorder the terms:
-5 + 4x + -1x2 = 15 + -15 + -5x + 5x + x2 + -1x2

Combine like terms: 15 + -15 = 0
-5 + 4x + -1x2 = 0 + -5x + 5x + x2 + -1x2
-5 + 4x + -1x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
-5 + 4x + -1x2 = 0 + x2 + -1x2
-5 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5 + 4x + -1x2 = 0

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

Divide each side by '-1'.
5 + -4x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -4x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -4x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x + x2 = 0 + -5
-4x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-4x + x2 = -5

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -5 + 4

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

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

Factor a perfect square on the left side:
(x + -2)(x + -2) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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