2X+3=(X+5)*(X+5)

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Solution for 2X+3=(X+5)*(X+5) equation: 


Simplifying
2X + 3 = (X + 5)(X + 5)

Reorder the terms:
3 + 2X = (X + 5)(X + 5)

Reorder the terms:
3 + 2X = (5 + X)(X + 5)

Reorder the terms:
3 + 2X = (5 + X)(5 + X)

Multiply (5 + X) * (5 + X)
3 + 2X = (5(5 + X) + X(5 + X))
3 + 2X = ((5 * 5 + X * 5) + X(5 + X))
3 + 2X = ((25 + 5X) + X(5 + X))
3 + 2X = (25 + 5X + (5 * X + X * X))
3 + 2X = (25 + 5X + (5X + X2))

Combine like terms: 5X + 5X = 10X
3 + 2X = (25 + 10X + X2)

Solving
3 + 2X = 25 + 10X + X2

Solving for variable 'X'.

Reorder the terms:
3 + -25 + 2X + -10X + -1X2 = 25 + 10X + X2 + -25 + -10X + -1X2

Combine like terms: 3 + -25 = -22
-22 + 2X + -10X + -1X2 = 25 + 10X + X2 + -25 + -10X + -1X2

Combine like terms: 2X + -10X = -8X
-22 + -8X + -1X2 = 25 + 10X + X2 + -25 + -10X + -1X2

Reorder the terms:
-22 + -8X + -1X2 = 25 + -25 + 10X + -10X + X2 + -1X2

Combine like terms: 25 + -25 = 0
-22 + -8X + -1X2 = 0 + 10X + -10X + X2 + -1X2
-22 + -8X + -1X2 = 10X + -10X + X2 + -1X2

Combine like terms: 10X + -10X = 0
-22 + -8X + -1X2 = 0 + X2 + -1X2
-22 + -8X + -1X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-22 + -8X + -1X2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(22 + 8X + X2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(22 + 8X + X2)' equal to zero and attempt to solve:

Simplifying
22 + 8X + X2 = 0

Solving
22 + 8X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + 8X + -22 + X2 = 0 + -22

Reorder the terms:
22 + -22 + 8X + X2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 8X + X2 = 0 + -22
8X + X2 = 0 + -22

Combine like terms: 0 + -22 = -22
8X + X2 = -22

The X term is 8X.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8X + 16 + X2 = -22 + 16

Reorder the terms:
16 + 8X + X2 = -22 + 16

Combine like terms: -22 + 16 = -6
16 + 8X + X2 = -6

Factor a perfect square on the left side:
(X + 4)(X + 4) = -6

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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