x^2+2=4x-3

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Solution for x^2+2=4x-3 equation:


Simplifying
x2 + 2 = 4x + -3

Reorder the terms:
2 + x2 = 4x + -3

Reorder the terms:
2 + x2 = -3 + 4x

Solving
2 + x2 = -3 + 4x

Solving for variable 'x'.

Reorder the terms:
2 + 3 + -4x + x2 = -3 + 4x + 3 + -4x

Combine like terms: 2 + 3 = 5
5 + -4x + x2 = -3 + 4x + 3 + -4x

Reorder the terms:
5 + -4x + x2 = -3 + 3 + 4x + -4x

Combine like terms: -3 + 3 = 0
5 + -4x + x2 = 0 + 4x + -4x
5 + -4x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
5 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -4x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -4x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x + x2 = 0 + -5
-4x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-4x + x2 = -5

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -5 + 4

Reorder the terms:
4 + -4x + x2 = -5 + 4

Combine like terms: -5 + 4 = -1
4 + -4x + x2 = -1

Factor a perfect square on the left side:
(x + -2)(x + -2) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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