x=x^2-6x+10

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Solution for x=x^2-6x+10 equation:


Simplifying
x = x2 + -6x + 10

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

Solving
x = 10 + -6x + x2

Solving for variable 'x'.

Reorder the terms:
-10 + x + 6x + -1x2 = 10 + -6x + x2 + -10 + 6x + -1x2

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

Reorder the terms:
-10 + 7x + -1x2 = 10 + -10 + -6x + 6x + x2 + -1x2

Combine like terms: 10 + -10 = 0
-10 + 7x + -1x2 = 0 + -6x + 6x + x2 + -1x2
-10 + 7x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-10 + 7x + -1x2 = 0 + x2 + -1x2
-10 + 7x + -1x2 = x2 + -1x2

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

Factor a trinomial.
(-5 + x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {5, 2}

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