5x^2-3x-62=0

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Solution for 5x^2-3x-62=0 equation: 


Simplifying
5x2 + -3x + -62 = 0

Reorder the terms:
-62 + -3x + 5x2 = 0

Solving
-62 + -3x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-12.4 + -0.6x + x2 = 0

Move the constant term to the right:

Add '12.4' to each side of the equation.
-12.4 + -0.6x + 12.4 + x2 = 0 + 12.4

Reorder the terms:
-12.4 + 12.4 + -0.6x + x2 = 0 + 12.4

Combine like terms: -12.4 + 12.4 = 0.0
0.0 + -0.6x + x2 = 0 + 12.4
-0.6x + x2 = 0 + 12.4

Combine like terms: 0 + 12.4 = 12.4
-0.6x + x2 = 12.4

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 12.4 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 12.4 + 0.09

Combine like terms: 12.4 + 0.09 = 12.49
0.09 + -0.6x + x2 = 12.49

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 12.49

Calculate the square root of the right side: 3.534119409

Break this problem into two subproblems by setting 
(x + -0.3) equal to 3.534119409 and -3.534119409.


Subproblem 1
x + -0.3 = 3.534119409

Simplifying
x + -0.3 = 3.534119409

Reorder the terms:
-0.3 + x = 3.534119409

Solving
-0.3 + x = 3.534119409

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = 3.534119409 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = 3.534119409 + 0.3
x = 3.534119409 + 0.3

Combine like terms: 3.534119409 + 0.3 = 3.834119409
x = 3.834119409

Simplifying
x = 3.834119409


Subproblem 2
x + -0.3 = -3.534119409

Simplifying
x + -0.3 = -3.534119409

Reorder the terms:
-0.3 + x = -3.534119409

Solving
-0.3 + x = -3.534119409

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = -3.534119409 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = -3.534119409 + 0.3
x = -3.534119409 + 0.3

Combine like terms: -3.534119409 + 0.3 = -3.234119409
x = -3.234119409

Simplifying
x = -3.234119409


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.834119409, -3.234119409}

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