x(5-2x)+x^2=6

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Solution for x(5-2x)+x^2=6 equation:


Simplifying
x(5 + -2x) + x2 = 6
(5 * x + -2x * x) + x2 = 6
(5x + -2x2) + x2 = 6

Combine like terms: -2x2 + x2 = -1x2
5x + -1x2 = 6

Solving
5x + -1x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 5x + -1x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 5x + -1x2 = 0

Factor a trinomial.
(-3 + x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3

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 = {3, 2}

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