368x-4.9x^2=1456

Solution for 368x-4.9x^2=1456 equation:

Simplifying
368x + -4.9x2 = 1456

Solving
368x + -4.9x2 = 1456

Solving for variable 'x'.

Reorder the terms:
-1456 + 368x + -4.9x2 = 1456 + -1456

Combine like terms: 1456 + -1456 = 0
-1456 + 368x + -4.9x2 = 0

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
297.1428571 + -75.10204082x + x2 = 0

Move the constant term to the right:

Add '-297.1428571' to each side of the equation.
297.1428571 + -75.10204082x + -297.1428571 + x2 = 0 + -297.1428571

Reorder the terms:
297.1428571 + -297.1428571 + -75.10204082x + x2 = 0 + -297.1428571

Combine like terms: 297.1428571 + -297.1428571 = 0.0000000
0.0000000 + -75.10204082x + x2 = 0 + -297.1428571
-75.10204082x + x2 = 0 + -297.1428571

Combine like terms: 0 + -297.1428571 = -297.1428571
-75.10204082x + x2 = -297.1428571

The x term is -75.10204082x.  Take half its coefficient (-37.55102041).
Square it (1410.079134) and add it to both sides.

Add '1410.079134' to each side of the equation.
-75.10204082x + 1410.079134 + x2 = -297.1428571 + 1410.079134

Reorder the terms:
1410.079134 + -75.10204082x + x2 = -297.1428571 + 1410.079134

Combine like terms: -297.1428571 + 1410.079134 = 1112.9362769
1410.079134 + -75.10204082x + x2 = 1112.9362769

Factor a perfect square on the left side:
(x + -37.55102041)(x + -37.55102041) = 1112.9362769

Calculate the square root of the right side: 33.360699586

Break this problem into two subproblems by setting 
(x + -37.55102041) equal to 33.360699586 and -33.360699586.

Subproblem 1
x + -37.55102041 = 33.360699586

Simplifying
x + -37.55102041 = 33.360699586

Reorder the terms:
-37.55102041 + x = 33.360699586

Solving
-37.55102041 + x = 33.360699586

Solving for variable 'x'.

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

Add '37.55102041' to each side of the equation.
-37.55102041 + 37.55102041 + x = 33.360699586 + 37.55102041

Combine like terms: -37.55102041 + 37.55102041 = 0.00000000
0.00000000 + x = 33.360699586 + 37.55102041
x = 33.360699586 + 37.55102041

Combine like terms: 33.360699586 + 37.55102041 = 70.911719996
x = 70.911719996

Simplifying
x = 70.911719996

Subproblem 2
x + -37.55102041 = -33.360699586

Simplifying
x + -37.55102041 = -33.360699586

Reorder the terms:
-37.55102041 + x = -33.360699586

Solving
-37.55102041 + x = -33.360699586

Solving for variable 'x'.

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

Add '37.55102041' to each side of the equation.
-37.55102041 + 37.55102041 + x = -33.360699586 + 37.55102041

Combine like terms: -37.55102041 + 37.55102041 = 0.00000000
0.00000000 + x = -33.360699586 + 37.55102041
x = -33.360699586 + 37.55102041

Combine like terms: -33.360699586 + 37.55102041 = 4.190320824
x = 4.190320824

Simplifying
x = 4.190320824

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {70.911719996, 4.190320824}