x^2-3.34x-46.7=0

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Solution for x^2-3.34x-46.7=0 equation: 


Simplifying
x2 + -3.34x + -46.7 = 0

Reorder the terms:
-46.7 + -3.34x + x2 = 0

Solving
-46.7 + -3.34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '46.7' to each side of the equation.
-46.7 + -3.34x + 46.7 + x2 = 0 + 46.7

Reorder the terms:
-46.7 + 46.7 + -3.34x + x2 = 0 + 46.7

Combine like terms: -46.7 + 46.7 = 0.0
0.0 + -3.34x + x2 = 0 + 46.7
-3.34x + x2 = 0 + 46.7

Combine like terms: 0 + 46.7 = 46.7
-3.34x + x2 = 46.7

The x term is -3.34x.  Take half its coefficient (-1.67).
Square it (2.7889) and add it to both sides.

Add '2.7889' to each side of the equation.
-3.34x + 2.7889 + x2 = 46.7 + 2.7889

Reorder the terms:
2.7889 + -3.34x + x2 = 46.7 + 2.7889

Combine like terms: 46.7 + 2.7889 = 49.4889
2.7889 + -3.34x + x2 = 49.4889

Factor a perfect square on the left side:
(x + -1.67)(x + -1.67) = 49.4889

Calculate the square root of the right side: 7.034834753

Break this problem into two subproblems by setting 
(x + -1.67) equal to 7.034834753 and -7.034834753.


Subproblem 1
x + -1.67 = 7.034834753

Simplifying
x + -1.67 = 7.034834753

Reorder the terms:
-1.67 + x = 7.034834753

Solving
-1.67 + x = 7.034834753

Solving for variable 'x'.

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

Add '1.67' to each side of the equation.
-1.67 + 1.67 + x = 7.034834753 + 1.67

Combine like terms: -1.67 + 1.67 = 0.00
0.00 + x = 7.034834753 + 1.67
x = 7.034834753 + 1.67

Combine like terms: 7.034834753 + 1.67 = 8.704834753
x = 8.704834753

Simplifying
x = 8.704834753


Subproblem 2
x + -1.67 = -7.034834753

Simplifying
x + -1.67 = -7.034834753

Reorder the terms:
-1.67 + x = -7.034834753

Solving
-1.67 + x = -7.034834753

Solving for variable 'x'.

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

Add '1.67' to each side of the equation.
-1.67 + 1.67 + x = -7.034834753 + 1.67

Combine like terms: -1.67 + 1.67 = 0.00
0.00 + x = -7.034834753 + 1.67
x = -7.034834753 + 1.67

Combine like terms: -7.034834753 + 1.67 = -5.364834753
x = -5.364834753

Simplifying
x = -5.364834753


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.704834753, -5.364834753}

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