1-3x=x^2+5x+32

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Solution for 1-3x=x^2+5x+32 equation: 


Simplifying
1 + -3x = x2 + 5x + 32

Reorder the terms:
1 + -3x = 32 + 5x + x2

Solving
1 + -3x = 32 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
1 + -32 + -3x + -5x + -1x2 = 32 + 5x + x2 + -32 + -5x + -1x2

Combine like terms: 1 + -32 = -31
-31 + -3x + -5x + -1x2 = 32 + 5x + x2 + -32 + -5x + -1x2

Combine like terms: -3x + -5x = -8x
-31 + -8x + -1x2 = 32 + 5x + x2 + -32 + -5x + -1x2

Reorder the terms:
-31 + -8x + -1x2 = 32 + -32 + 5x + -5x + x2 + -1x2

Combine like terms: 32 + -32 = 0
-31 + -8x + -1x2 = 0 + 5x + -5x + x2 + -1x2
-31 + -8x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
-31 + -8x + -1x2 = 0 + x2 + -1x2
-31 + -8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-31 + -8x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(31 + 8x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(31 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
31 + 8x + x2 = 0

Solving
31 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + 8x + -31 + x2 = 0 + -31

Reorder the terms:
31 + -31 + 8x + x2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + 8x + x2 = 0 + -31
8x + x2 = 0 + -31

Combine like terms: 0 + -31 = -31
8x + x2 = -31

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 = -31 + 16

Reorder the terms:
16 + 8x + x2 = -31 + 16

Combine like terms: -31 + 16 = -15
16 + 8x + x2 = -15

Factor a perfect square on the left side:
(x + 4)(x + 4) = -15

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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