3-4x=5(x^2+2)

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Solution for 3-4x=5(x^2+2) equation: 


Simplifying
3 + -4x = 5(x2 + 2)

Reorder the terms:
3 + -4x = 5(2 + x2)
3 + -4x = (2 * 5 + x2 * 5)
3 + -4x = (10 + 5x2)

Solving
3 + -4x = 10 + 5x2

Solving for variable 'x'.

Reorder the terms:
3 + -10 + -4x + -5x2 = 10 + 5x2 + -10 + -5x2

Combine like terms: 3 + -10 = -7
-7 + -4x + -5x2 = 10 + 5x2 + -10 + -5x2

Reorder the terms:
-7 + -4x + -5x2 = 10 + -10 + 5x2 + -5x2

Combine like terms: 10 + -10 = 0
-7 + -4x + -5x2 = 0 + 5x2 + -5x2
-7 + -4x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-7 + -4x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 4x + 5x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + 4x + 5x2)' equal to zero and attempt to solve:

Simplifying
7 + 4x + 5x2 = 0

Solving
7 + 4x + 5x2 = 0

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

Divide each side by '5'.
1.4 + 0.8x + x2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + 0.8x + -1.4 + x2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + 0.8x + x2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + 0.8x + x2 = 0 + -1.4
0.8x + x2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
0.8x + x2 = -1.4

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = -1.4 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = -1.4 + 0.16

Combine like terms: -1.4 + 0.16 = -1.24
0.16 + 0.8x + x2 = -1.24

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = -1.24

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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