463x^2+628x-7119=0

Solution for 463x^2+628x-7119=0 equation:

Simplifying
463x2 + 628x + -7119 = 0

Reorder the terms:
-7119 + 628x + 463x2 = 0

Solving
-7119 + 628x + 463x2 = 0

Solving for variable 'x'.

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

Divide each side by '463'.
-15.37580994 + 1.35637149x + x2 = 0

Move the constant term to the right:

Add '15.37580994' to each side of the equation.
-15.37580994 + 1.35637149x + 15.37580994 + x2 = 0 + 15.37580994

Reorder the terms:
-15.37580994 + 15.37580994 + 1.35637149x + x2 = 0 + 15.37580994

Combine like terms: -15.37580994 + 15.37580994 = 0.00000000
0.00000000 + 1.35637149x + x2 = 0 + 15.37580994
1.35637149x + x2 = 0 + 15.37580994

Combine like terms: 0 + 15.37580994 = 15.37580994
1.35637149x + x2 = 15.37580994

The x term is 1.35637149x.  Take half its coefficient (0.678185745).
Square it (0.4599359047) and add it to both sides.

Add '0.4599359047' to each side of the equation.
1.35637149x + 0.4599359047 + x2 = 15.37580994 + 0.4599359047

Reorder the terms:
0.4599359047 + 1.35637149x + x2 = 15.37580994 + 0.4599359047

Combine like terms: 15.37580994 + 0.4599359047 = 15.8357458447
0.4599359047 + 1.35637149x + x2 = 15.8357458447

Factor a perfect square on the left side:
(x + 0.678185745)(x + 0.678185745) = 15.8357458447

Calculate the square root of the right side: 3.979415264

Break this problem into two subproblems by setting 
(x + 0.678185745) equal to 3.979415264 and -3.979415264.

Subproblem 1
x + 0.678185745 = 3.979415264

Simplifying
x + 0.678185745 = 3.979415264

Reorder the terms:
0.678185745 + x = 3.979415264

Solving
0.678185745 + x = 3.979415264

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.678185745' to each side of the equation.
0.678185745 + -0.678185745 + x = 3.979415264 + -0.678185745

Combine like terms: 0.678185745 + -0.678185745 = 0.000000000
0.000000000 + x = 3.979415264 + -0.678185745
x = 3.979415264 + -0.678185745

Combine like terms: 3.979415264 + -0.678185745 = 3.301229519
x = 3.301229519

Simplifying
x = 3.301229519

Subproblem 2
x + 0.678185745 = -3.979415264

Simplifying
x + 0.678185745 = -3.979415264

Reorder the terms:
0.678185745 + x = -3.979415264

Solving
0.678185745 + x = -3.979415264

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.678185745' to each side of the equation.
0.678185745 + -0.678185745 + x = -3.979415264 + -0.678185745

Combine like terms: 0.678185745 + -0.678185745 = 0.000000000
0.000000000 + x = -3.979415264 + -0.678185745
x = -3.979415264 + -0.678185745

Combine like terms: -3.979415264 + -0.678185745 = -4.657601009
x = -4.657601009

Simplifying
x = -4.657601009

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.301229519, -4.657601009}