0.03x^2-2.4(x)+46=0

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Solution for 0.03x^2-2.4(x)+46=0 equation: 


Simplifying
0.03x2 + -2.4(x) + 46 = 0

Reorder the terms:
46 + -2.4x + 0.03x2 = 0

Solving
46 + -2.4x + 0.03x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.03'.
1533.333333 + -80x + x2 = 0

Move the constant term to the right:

Add '-1533.333333' to each side of the equation.
1533.333333 + -80x + -1533.333333 + x2 = 0 + -1533.333333

Reorder the terms:
1533.333333 + -1533.333333 + -80x + x2 = 0 + -1533.333333

Combine like terms: 1533.333333 + -1533.333333 = 0.000000
0.000000 + -80x + x2 = 0 + -1533.333333
-80x + x2 = 0 + -1533.333333

Combine like terms: 0 + -1533.333333 = -1533.333333
-80x + x2 = -1533.333333

The x term is -80x.  Take half its coefficient (-40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
-80x + 1600 + x2 = -1533.333333 + 1600

Reorder the terms:
1600 + -80x + x2 = -1533.333333 + 1600

Combine like terms: -1533.333333 + 1600 = 66.666667
1600 + -80x + x2 = 66.666667

Factor a perfect square on the left side:
(x + -40)(x + -40) = 66.666667

Calculate the square root of the right side: 8.16496583

Break this problem into two subproblems by setting 
(x + -40) equal to 8.16496583 and -8.16496583.


Subproblem 1
x + -40 = 8.16496583

Simplifying
x + -40 = 8.16496583

Reorder the terms:
-40 + x = 8.16496583

Solving
-40 + x = 8.16496583

Solving for variable 'x'.

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

Add '40' to each side of the equation.
-40 + 40 + x = 8.16496583 + 40

Combine like terms: -40 + 40 = 0
0 + x = 8.16496583 + 40
x = 8.16496583 + 40

Combine like terms: 8.16496583 + 40 = 48.16496583
x = 48.16496583

Simplifying
x = 48.16496583


Subproblem 2
x + -40 = -8.16496583

Simplifying
x + -40 = -8.16496583

Reorder the terms:
-40 + x = -8.16496583

Solving
-40 + x = -8.16496583

Solving for variable 'x'.

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

Add '40' to each side of the equation.
-40 + 40 + x = -8.16496583 + 40

Combine like terms: -40 + 40 = 0
0 + x = -8.16496583 + 40
x = -8.16496583 + 40

Combine like terms: -8.16496583 + 40 = 31.83503417
x = 31.83503417

Simplifying
x = 31.83503417


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {48.16496583, 31.83503417}

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