x(u+3)-x=9+x(u-x)

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Solution for x(u+3)-x=9+x(u-x) equation:


Simplifying
x(u + 3) + -1x = 9 + x(u + -1x)

Reorder the terms:
x(3 + u) + -1x = 9 + x(u + -1x)
(3 * x + u * x) + -1x = 9 + x(u + -1x)

Reorder the terms:
(ux + 3x) + -1x = 9 + x(u + -1x)
(ux + 3x) + -1x = 9 + x(u + -1x)

Combine like terms: 3x + -1x = 2x
ux + 2x = 9 + x(u + -1x)
ux + 2x = 9 + (u * x + -1x * x)
ux + 2x = 9 + (ux + -1x2)

Add '-1ux' to each side of the equation.
ux + -1ux + 2x = 9 + ux + -1ux + -1x2

Combine like terms: ux + -1ux = 0
0 + 2x = 9 + ux + -1ux + -1x2
2x = 9 + ux + -1ux + -1x2

Combine like terms: ux + -1ux = 0
2x = 9 + 0 + -1x2
2x = 9 + -1x2

Solving
2x = 9 + -1x2

Solving for variable 'x'.

Reorder the terms:
-9 + 2x + x2 = 9 + -1x2 + -9 + x2

Reorder the terms:
-9 + 2x + x2 = 9 + -9 + -1x2 + x2

Combine like terms: 9 + -9 = 0
-9 + 2x + x2 = 0 + -1x2 + x2
-9 + 2x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-9 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 2x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 2x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2x + x2 = 0 + 9
2x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
2x + x2 = 9

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 9 + 1

Reorder the terms:
1 + 2x + x2 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + 2x + x2 = 10

Factor a perfect square on the left side:
(x + 1)(x + 1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 1) equal to 3.16227766 and -3.16227766.

Subproblem 1

x + 1 = 3.16227766 Simplifying x + 1 = 3.16227766 Reorder the terms: 1 + x = 3.16227766 Solving 1 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.16227766 + -1 x = 3.16227766 + -1 Combine like terms: 3.16227766 + -1 = 2.16227766 x = 2.16227766 Simplifying x = 2.16227766

Subproblem 2

x + 1 = -3.16227766 Simplifying x + 1 = -3.16227766 Reorder the terms: 1 + x = -3.16227766 Solving 1 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.16227766 + -1 x = -3.16227766 + -1 Combine like terms: -3.16227766 + -1 = -4.16227766 x = -4.16227766 Simplifying x = -4.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.16227766, -4.16227766}

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