0.62x^2+0.5x=18

Solution for 0.62x^2+0.5x=18 equation:

Simplifying
0.62x2 + 0.5x = 18

Reorder the terms:
0.5x + 0.62x2 = 18

Solving
0.5x + 0.62x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + 0.5x + 0.62x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 0.5x + 0.62x2 = 0

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

Divide each side by '0.62'.
-29.03225806 + 0.8064516129x + x2 = 0

Move the constant term to the right:

Add '29.03225806' to each side of the equation.
-29.03225806 + 0.8064516129x + 29.03225806 + x2 = 0 + 29.03225806

Reorder the terms:
-29.03225806 + 29.03225806 + 0.8064516129x + x2 = 0 + 29.03225806

Combine like terms: -29.03225806 + 29.03225806 = 0.00000000
0.00000000 + 0.8064516129x + x2 = 0 + 29.03225806
0.8064516129x + x2 = 0 + 29.03225806

Combine like terms: 0 + 29.03225806 = 29.03225806
0.8064516129x + x2 = 29.03225806

The x term is 0.8064516129x.  Take half its coefficient (0.4032258065).
Square it (0.1625910510) and add it to both sides.

Add '0.1625910510' to each side of the equation.
0.8064516129x + 0.1625910510 + x2 = 29.03225806 + 0.1625910510

Reorder the terms:
0.1625910510 + 0.8064516129x + x2 = 29.03225806 + 0.1625910510

Combine like terms: 29.03225806 + 0.1625910510 = 29.194849111
0.1625910510 + 0.8064516129x + x2 = 29.194849111

Factor a perfect square on the left side:
(x + 0.4032258065)(x + 0.4032258065) = 29.194849111

Calculate the square root of the right side: 5.403225806

Break this problem into two subproblems by setting 
(x + 0.4032258065) equal to 5.403225806 and -5.403225806.

Subproblem 1
x + 0.4032258065 = 5.403225806

Simplifying
x + 0.4032258065 = 5.403225806

Reorder the terms:
0.4032258065 + x = 5.403225806

Solving
0.4032258065 + x = 5.403225806

Solving for variable 'x'.

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

Add '-0.4032258065' to each side of the equation.
0.4032258065 + -0.4032258065 + x = 5.403225806 + -0.4032258065

Combine like terms: 0.4032258065 + -0.4032258065 = 0.0000000000
0.0000000000 + x = 5.403225806 + -0.4032258065
x = 5.403225806 + -0.4032258065

Combine like terms: 5.403225806 + -0.4032258065 = 4.9999999995
x = 4.9999999995

Simplifying
x = 4.9999999995

Subproblem 2
x + 0.4032258065 = -5.403225806

Simplifying
x + 0.4032258065 = -5.403225806

Reorder the terms:
0.4032258065 + x = -5.403225806

Solving
0.4032258065 + x = -5.403225806

Solving for variable 'x'.

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

Add '-0.4032258065' to each side of the equation.
0.4032258065 + -0.4032258065 + x = -5.403225806 + -0.4032258065

Combine like terms: 0.4032258065 + -0.4032258065 = 0.0000000000
0.0000000000 + x = -5.403225806 + -0.4032258065
x = -5.403225806 + -0.4032258065

Combine like terms: -5.403225806 + -0.4032258065 = -5.8064516125
x = -5.8064516125

Simplifying
x = -5.8064516125

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.9999999995, -5.8064516125}