x^2+0.0000152x-0.0000000053049=0

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Solution for x^2+0.0000152x-0.0000000053049=0 equation: 


Simplifying
x2 + 0.0000152x + -0.0000000053049 = 0

Reorder the terms:
-0.0000000053049 + 0.0000152x + x2 = 0

Solving
-0.0000000053049 + 0.0000152x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.0000000053049' to each side of the equation.
-0.0000000053049 + 0.0000152x + 0.0000000053049 + x2 = 0 + 0.0000000053049

Reorder the terms:
-0.0000000053049 + 0.0000000053049 + 0.0000152x + x2 = 0 + 0.0000000053049

Combine like terms: -0.0000000053049 + 0.0000000053049 = 0.0000000000000
0.0000000000000 + 0.0000152x + x2 = 0 + 0.0000000053049
0.0000152x + x2 = 0 + 0.0000000053049

Combine like terms: 0 + 0.0000000053049 = 0.0000000053049
0.0000152x + x2 = 0.0000000053049

The x term is 0.0000152x.  Take half its coefficient (0.0000076).
Square it (0.00000000005776) and add it to both sides.

Add '0.00000000005776' to each side of the equation.
0.0000152x + 0.00000000005776 + x2 = 0.0000000053049 + 0.00000000005776

Reorder the terms:
0.00000000005776 + 0.0000152x + x2 = 0.0000000053049 + 0.00000000005776

Combine like terms: 0.0000000053049 + 0.00000000005776 = 0.00000000536266
0.00000000005776 + 0.0000152x + x2 = 0.00000000536266

Factor a perfect square on the left side:
(x + 0.0000076)(x + 0.0000076) = 0.00000000536266

Calculate the square root of the right side: 0.00007323

Break this problem into two subproblems by setting 
(x + 0.0000076) equal to 0.00007323 and -0.00007323.


Subproblem 1
x + 0.0000076 = 0.00007323

Simplifying
x + 0.0000076 = 0.00007323

Reorder the terms:
0.0000076 + x = 0.00007323

Solving
0.0000076 + x = 0.00007323

Solving for variable 'x'.

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

Add '-0.0000076' to each side of the equation.
0.0000076 + -0.0000076 + x = 0.00007323 + -0.0000076

Combine like terms: 0.0000076 + -0.0000076 = 0.0000000
0.0000000 + x = 0.00007323 + -0.0000076
x = 0.00007323 + -0.0000076

Combine like terms: 0.00007323 + -0.0000076 = 0.00006563
x = 0.00006563

Simplifying
x = 0.00006563


Subproblem 2
x + 0.0000076 = -0.00007323

Simplifying
x + 0.0000076 = -0.00007323

Reorder the terms:
0.0000076 + x = -0.00007323

Solving
0.0000076 + x = -0.00007323

Solving for variable 'x'.

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

Add '-0.0000076' to each side of the equation.
0.0000076 + -0.0000076 + x = -0.00007323 + -0.0000076

Combine like terms: 0.0000076 + -0.0000076 = 0.0000000
0.0000000 + x = -0.00007323 + -0.0000076
x = -0.00007323 + -0.0000076

Combine like terms: -0.00007323 + -0.0000076 = -0.00008083
x = -0.00008083

Simplifying
x = -0.00008083


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.00006563, -0.00008083}

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