60=40x+9.81x^2

Solution for 60=40x+9.81x^2 equation:

Simplifying
60 = 40x + 9.81x2

Solving
60 = 40x + 9.81x2

Solving for variable 'x'.

Reorder the terms:
60 + -40x + -9.81x2 = 40x + -40x + 9.81x2 + -9.81x2

Combine like terms: 40x + -40x = 0
60 + -40x + -9.81x2 = 0 + 9.81x2 + -9.81x2
60 + -40x + -9.81x2 = 9.81x2 + -9.81x2

Combine like terms: 9.81x2 + -9.81x2 = 0.00
60 + -40x + -9.81x2 = 0.00

Begin completing the square.  Divide all terms by
-9.81 the coefficient of the squared term: 

Divide each side by '-9.81'.
-6.116207951 + 4.077471967x + x2 = 0

Move the constant term to the right:

Add '6.116207951' to each side of the equation.
-6.116207951 + 4.077471967x + 6.116207951 + x2 = 0 + 6.116207951

Reorder the terms:
-6.116207951 + 6.116207951 + 4.077471967x + x2 = 0 + 6.116207951

Combine like terms: -6.116207951 + 6.116207951 = 0.000000000
0.000000000 + 4.077471967x + x2 = 0 + 6.116207951
4.077471967x + x2 = 0 + 6.116207951

Combine like terms: 0 + 6.116207951 = 6.116207951
4.077471967x + x2 = 6.116207951

The x term is 4.077471967x.  Take half its coefficient (2.038735984).
Square it (4.156444412) and add it to both sides.

Add '4.156444412' to each side of the equation.
4.077471967x + 4.156444412 + x2 = 6.116207951 + 4.156444412

Reorder the terms:
4.156444412 + 4.077471967x + x2 = 6.116207951 + 4.156444412

Combine like terms: 6.116207951 + 4.156444412 = 10.272652363
4.156444412 + 4.077471967x + x2 = 10.272652363

Factor a perfect square on the left side:
(x + 2.038735984)(x + 2.038735984) = 10.272652363

Calculate the square root of the right side: 3.205097871

Break this problem into two subproblems by setting 
(x + 2.038735984) equal to 3.205097871 and -3.205097871.

Subproblem 1
x + 2.038735984 = 3.205097871

Simplifying
x + 2.038735984 = 3.205097871

Reorder the terms:
2.038735984 + x = 3.205097871

Solving
2.038735984 + x = 3.205097871

Solving for variable 'x'.

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

Add '-2.038735984' to each side of the equation.
2.038735984 + -2.038735984 + x = 3.205097871 + -2.038735984

Combine like terms: 2.038735984 + -2.038735984 = 0.000000000
0.000000000 + x = 3.205097871 + -2.038735984
x = 3.205097871 + -2.038735984

Combine like terms: 3.205097871 + -2.038735984 = 1.166361887
x = 1.166361887

Simplifying
x = 1.166361887

Subproblem 2
x + 2.038735984 = -3.205097871

Simplifying
x + 2.038735984 = -3.205097871

Reorder the terms:
2.038735984 + x = -3.205097871

Solving
2.038735984 + x = -3.205097871

Solving for variable 'x'.

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

Add '-2.038735984' to each side of the equation.
2.038735984 + -2.038735984 + x = -3.205097871 + -2.038735984

Combine like terms: 2.038735984 + -2.038735984 = 0.000000000
0.000000000 + x = -3.205097871 + -2.038735984
x = -3.205097871 + -2.038735984

Combine like terms: -3.205097871 + -2.038735984 = -5.243833855
x = -5.243833855

Simplifying
x = -5.243833855

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.166361887, -5.243833855}