22-2x=-x^2+8x-3

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Solution for 22-2x=-x^2+8x-3 equation:


Simplifying
22 + -2x = -1x2 + 8x + -3

Reorder the terms:
22 + -2x = -3 + 8x + -1x2

Solving
22 + -2x = -3 + 8x + -1x2

Solving for variable 'x'.

Reorder the terms:
22 + 3 + -2x + -8x + x2 = -3 + 8x + -1x2 + 3 + -8x + x2

Combine like terms: 22 + 3 = 25
25 + -2x + -8x + x2 = -3 + 8x + -1x2 + 3 + -8x + x2

Combine like terms: -2x + -8x = -10x
25 + -10x + x2 = -3 + 8x + -1x2 + 3 + -8x + x2

Reorder the terms:
25 + -10x + x2 = -3 + 3 + 8x + -8x + -1x2 + x2

Combine like terms: -3 + 3 = 0
25 + -10x + x2 = 0 + 8x + -8x + -1x2 + x2
25 + -10x + x2 = 8x + -8x + -1x2 + x2

Combine like terms: 8x + -8x = 0
25 + -10x + x2 = 0 + -1x2 + x2
25 + -10x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
25 + -10x + x2 = 0

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

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {5, 5}

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