4x^2+10x+106=0

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Solution for 4x^2+10x+106=0 equation: 


Simplifying
4x2 + 10x + 106 = 0

Reorder the terms:
106 + 10x + 4x2 = 0

Solving
106 + 10x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(53 + 5x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(53 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
53 + 5x + 2x2 = 0

Solving
53 + 5x + 2x2 = 0

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

Divide each side by '2'.
26.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '-26.5' to each side of the equation.
26.5 + 2.5x + -26.5 + x2 = 0 + -26.5

Reorder the terms:
26.5 + -26.5 + 2.5x + x2 = 0 + -26.5

Combine like terms: 26.5 + -26.5 = 0.0
0.0 + 2.5x + x2 = 0 + -26.5
2.5x + x2 = 0 + -26.5

Combine like terms: 0 + -26.5 = -26.5
2.5x + x2 = -26.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = -26.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = -26.5 + 1.5625

Combine like terms: -26.5 + 1.5625 = -24.9375
1.5625 + 2.5x + x2 = -24.9375

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = -24.9375

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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