-5x^2-4.66x=-50

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Solution for -5x^2-4.66x=-50 equation:


Simplifying
-5x2 + -4.66x = -50

Reorder the terms:
-4.66x + -5x2 = -50

Solving
-4.66x + -5x2 = -50

Solving for variable 'x'.

Reorder the terms:
50 + -4.66x + -5x2 = -50 + 50

Combine like terms: -50 + 50 = 0
50 + -4.66x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-10 + 0.932x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 0.932x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 0.932x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 0.932x + x2 = 0 + 10
0.932x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
0.932x + x2 = 10

The x term is 0.932x.  Take half its coefficient (0.466).
Square it (0.217156) and add it to both sides.

Add '0.217156' to each side of the equation.
0.932x + 0.217156 + x2 = 10 + 0.217156

Reorder the terms:
0.217156 + 0.932x + x2 = 10 + 0.217156

Combine like terms: 10 + 0.217156 = 10.217156
0.217156 + 0.932x + x2 = 10.217156

Factor a perfect square on the left side:
(x + 0.466)(x + 0.466) = 10.217156

Calculate the square root of the right side: 3.196428632

Break this problem into two subproblems by setting 
(x + 0.466) equal to 3.196428632 and -3.196428632.


Subproblem 1
x + 0.466 = 3.196428632

Simplifying
x + 0.466 = 3.196428632

Reorder the terms:
0.466 + x = 3.196428632

Solving
0.466 + x = 3.196428632

Solving for variable 'x'.

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

Add '-0.466' to each side of the equation.
0.466 + -0.466 + x = 3.196428632 + -0.466

Combine like terms: 0.466 + -0.466 = 0.000
0.000 + x = 3.196428632 + -0.466
x = 3.196428632 + -0.466

Combine like terms: 3.196428632 + -0.466 = 2.730428632
x = 2.730428632

Simplifying
x = 2.730428632


Subproblem 2
x + 0.466 = -3.196428632

Simplifying
x + 0.466 = -3.196428632

Reorder the terms:
0.466 + x = -3.196428632

Solving
0.466 + x = -3.196428632

Solving for variable 'x'.

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

Add '-0.466' to each side of the equation.
0.466 + -0.466 + x = -3.196428632 + -0.466

Combine like terms: 0.466 + -0.466 = 0.000
0.000 + x = -3.196428632 + -0.466
x = -3.196428632 + -0.466

Combine like terms: -3.196428632 + -0.466 = -3.662428632
x = -3.662428632

Simplifying
x = -3.662428632


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.730428632, -3.662428632}

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