2x^2=x^2+1.75-3x

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Solution for 2x^2=x^2+1.75-3x equation: 


Simplifying
2x2 = x2 + 1.75 + -3x

Reorder the terms:
2x2 = 1.75 + -3x + x2

Solving
2x2 = 1.75 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
-1.75 + 3x + 2x2 + -1x2 = 1.75 + -3x + x2 + -1.75 + 3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-1.75 + 3x + 1x2 = 1.75 + -3x + x2 + -1.75 + 3x + -1x2

Reorder the terms:
-1.75 + 3x + 1x2 = 1.75 + -1.75 + -3x + 3x + x2 + -1x2

Combine like terms: 1.75 + -1.75 = 0.00
-1.75 + 3x + 1x2 = 0.00 + -3x + 3x + x2 + -1x2
-1.75 + 3x + 1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
-1.75 + 3x + 1x2 = 0 + x2 + -1x2
-1.75 + 3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1.75 + 3x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 3x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 3x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 3x + x2 = 0 + 1.75
3x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
3x + x2 = 1.75

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 1.75 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 1.75 + 2.25

Combine like terms: 1.75 + 2.25 = 4
2.25 + 3x + x2 = 4

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2 and -2.


Subproblem 1
x + 1.5 = 2

Simplifying
x + 1.5 = 2

Reorder the terms:
1.5 + x = 2

Solving
1.5 + x = 2

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 2 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2 + -1.5
x = 2 + -1.5

Combine like terms: 2 + -1.5 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + 1.5 = -2

Simplifying
x + 1.5 = -2

Reorder the terms:
1.5 + x = -2

Solving
1.5 + x = -2

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -2 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2 + -1.5
x = -2 + -1.5

Combine like terms: -2 + -1.5 = -3.5
x = -3.5

Simplifying
x = -3.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -3.5}

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