7x+3x^2-1625=0

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Solution for 7x+3x^2-1625=0 equation: 


Simplifying
7x + 3x2 + -1625 = 0

Reorder the terms:
-1625 + 7x + 3x2 = 0

Solving
-1625 + 7x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-541.6666667 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '541.6666667' to each side of the equation.
-541.6666667 + 2.333333333x + 541.6666667 + x2 = 0 + 541.6666667

Reorder the terms:
-541.6666667 + 541.6666667 + 2.333333333x + x2 = 0 + 541.6666667

Combine like terms: -541.6666667 + 541.6666667 = 0.0000000
0.0000000 + 2.333333333x + x2 = 0 + 541.6666667
2.333333333x + x2 = 0 + 541.6666667

Combine like terms: 0 + 541.6666667 = 541.6666667
2.333333333x + x2 = 541.6666667

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 541.6666667 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 541.6666667 + 1.361111112

Combine like terms: 541.6666667 + 1.361111112 = 543.027777812
1.361111112 + 2.333333333x + x2 = 543.027777812

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 543.027777812

Calculate the square root of the right side: 23.302956418

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 23.302956418 and -23.302956418.


Subproblem 1
x + 1.166666667 = 23.302956418

Simplifying
x + 1.166666667 = 23.302956418

Reorder the terms:
1.166666667 + x = 23.302956418

Solving
1.166666667 + x = 23.302956418

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 23.302956418 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 23.302956418 + -1.166666667
x = 23.302956418 + -1.166666667

Combine like terms: 23.302956418 + -1.166666667 = 22.136289751
x = 22.136289751

Simplifying
x = 22.136289751


Subproblem 2
x + 1.166666667 = -23.302956418

Simplifying
x + 1.166666667 = -23.302956418

Reorder the terms:
1.166666667 + x = -23.302956418

Solving
1.166666667 + x = -23.302956418

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -23.302956418 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -23.302956418 + -1.166666667
x = -23.302956418 + -1.166666667

Combine like terms: -23.302956418 + -1.166666667 = -24.469623085
x = -24.469623085

Simplifying
x = -24.469623085


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.136289751, -24.469623085}

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