0=10-7x+x^2

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Solution for 0=10-7x+x^2 equation:


Simplifying
0 = 10 + -7x + x2

Solving
0 = 10 + -7x + x2

Solving for variable 'x'.

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

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

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

Combine like terms: -7x + 7x = 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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