x+10(3)=x(2)x(2)+10

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Solution for x+10(3)=x(2)x(2)+10 equation: 


Simplifying
x + 10(3) = x(2) * x(2) + 10

Multiply 10 * 3
x + 30 = x(2) * x(2) + 10

Reorder the terms:
30 + x = x(2) * x(2) + 10

Reorder the terms for easier multiplication:
30 + x = 2 * 2x * x + 10

Multiply 2 * 2
30 + x = 4x * x + 10

Multiply x * x
30 + x = 4x2 + 10

Reorder the terms:
30 + x = 10 + 4x2

Solving
30 + x = 10 + 4x2

Solving for variable 'x'.

Reorder the terms:
30 + -10 + x + -4x2 = 10 + 4x2 + -10 + -4x2

Combine like terms: 30 + -10 = 20
20 + x + -4x2 = 10 + 4x2 + -10 + -4x2

Reorder the terms:
20 + x + -4x2 = 10 + -10 + 4x2 + -4x2

Combine like terms: 10 + -10 = 0
20 + x + -4x2 = 0 + 4x2 + -4x2
20 + x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
20 + x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-5 + -0.25x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -0.25x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -0.25x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -0.25x + x2 = 0 + 5
-0.25x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-0.25x + x2 = 5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.25x + 0.25 + x2 = 5 + 0.25

Reorder the terms:
0.25 + -0.25x + x2 = 5 + 0.25

Combine like terms: 5 + 0.25 = 5.25
0.25 + -0.25x + x2 = 5.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.291287847 and -2.291287847.


Subproblem 1
x + 0.5 = 2.291287847

Simplifying
x + 0.5 = 2.291287847

Reorder the terms:
0.5 + x = 2.291287847

Solving
0.5 + x = 2.291287847

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.291287847 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.291287847 + -0.5
x = 2.291287847 + -0.5

Combine like terms: 2.291287847 + -0.5 = 1.791287847
x = 1.791287847

Simplifying
x = 1.791287847


Subproblem 2
x + 0.5 = -2.291287847

Simplifying
x + 0.5 = -2.291287847

Reorder the terms:
0.5 + x = -2.291287847

Solving
0.5 + x = -2.291287847

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.291287847 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.291287847 + -0.5
x = -2.291287847 + -0.5

Combine like terms: -2.291287847 + -0.5 = -2.791287847
x = -2.791287847

Simplifying
x = -2.791287847


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.791287847, -2.791287847}

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