0=5x^2+14x+53

Solution for 0=5x^2+14x+53 equation:

Simplifying
0 = 5x2 + 14x + 53

Reorder the terms:
0 = 53 + 14x + 5x2

Solving
0 = 53 + 14x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + -53 = -53
-53 + -14x + -5x2 = 53 + 14x + 5x2 + -53 + -14x + -5x2

Reorder the terms:
-53 + -14x + -5x2 = 53 + -53 + 14x + -14x + 5x2 + -5x2

Combine like terms: 53 + -53 = 0
-53 + -14x + -5x2 = 0 + 14x + -14x + 5x2 + -5x2
-53 + -14x + -5x2 = 14x + -14x + 5x2 + -5x2

Combine like terms: 14x + -14x = 0
-53 + -14x + -5x2 = 0 + 5x2 + -5x2
-53 + -14x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-53 + -14x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(53 + 14x + 5x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(53 + 14x + 5x2)' equal to zero and attempt to solve:

Simplifying
53 + 14x + 5x2 = 0

Solving
53 + 14x + 5x2 = 0

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

Divide each side by '5'.
10.6 + 2.8x + x2 = 0

Move the constant term to the right:

Add '-10.6' to each side of the equation.
10.6 + 2.8x + -10.6 + x2 = 0 + -10.6

Reorder the terms:
10.6 + -10.6 + 2.8x + x2 = 0 + -10.6

Combine like terms: 10.6 + -10.6 = 0.0
0.0 + 2.8x + x2 = 0 + -10.6
2.8x + x2 = 0 + -10.6

Combine like terms: 0 + -10.6 = -10.6
2.8x + x2 = -10.6

The x term is 2.8x.  Take half its coefficient (1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
2.8x + 1.96 + x2 = -10.6 + 1.96

Reorder the terms:
1.96 + 2.8x + x2 = -10.6 + 1.96

Combine like terms: -10.6 + 1.96 = -8.64
1.96 + 2.8x + x2 = -8.64

Factor a perfect square on the left side:
(x + 1.4)(x + 1.4) = -8.64

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.