(x^2)+(.000018x)-(.00000288)=0

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Solution for (x^2)+(.000018x)-(.00000288)=0 equation:


Simplifying
(x2) + (0.000018x) + -1(0.00000288) = 0
x2 + (0.000018x) + -1(0.00000288) = 0

Multiply -1 * 0.00000288
x2 + (0.000018x) + -0.00000288 = 0

Reorder the terms:
-0.00000288 + (0.000018x) + x2 = 0

Solving
-0.00000288 + (0.000018x) + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.00000288' to each side of the equation.
-0.00000288 + (0.000018x) + 0.00000288 + x2 = 0 + 0.00000288

Reorder the terms:
-0.00000288 + 0.00000288 + (0.000018x) + x2 = 0 + 0.00000288

Combine like terms: -0.00000288 + 0.00000288 = 0.00000000
0.00000000 + (0.000018x) + x2 = 0 + 0.00000288
(0.000018x) + x2 = 0 + 0.00000288

Combine like terms: 0 + 0.00000288 = 0.00000288
(0.000018x) + x2 = 0.00000288

The x term is (0.000018x).  Take half its coefficient (0.000009).
Square it (0.000000000081) and add it to both sides.

Add '0.000000000081' to each side of the equation.
(0.000018x) + 0.000000000081 + x2 = 0.00000288 + 0.000000000081

Reorder the terms:
0.000000000081 + (0.000018x) + x2 = 0.00000288 + 0.000000000081

Combine like terms: 0.00000288 + 0.000000000081 = 0.000002880081
0.000000000081 + (0.000018x) + x2 = 0.000002880081

Factor a perfect square on the left side:
(x + 0.000009)(x + 0.000009) = 0.000002880081

Calculate the square root of the right side: 0.00169708

Break this problem into two subproblems by setting 
(x + 0.000009) equal to 0.00169708 and -0.00169708.

Subproblem 1

x + 0.000009 = 0.00169708 Simplifying x + 0.000009 = 0.00169708 Reorder the terms: 0.000009 + x = 0.00169708 Solving 0.000009 + x = 0.00169708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000009' to each side of the equation. 0.000009 + -0.000009 + x = 0.00169708 + -0.000009 Combine like terms: 0.000009 + -0.000009 = 0.000000 0.000000 + x = 0.00169708 + -0.000009 x = 0.00169708 + -0.000009 Combine like terms: 0.00169708 + -0.000009 = 0.00168808 x = 0.00168808 Simplifying x = 0.00168808

Subproblem 2

x + 0.000009 = -0.00169708 Simplifying x + 0.000009 = -0.00169708 Reorder the terms: 0.000009 + x = -0.00169708 Solving 0.000009 + x = -0.00169708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000009' to each side of the equation. 0.000009 + -0.000009 + x = -0.00169708 + -0.000009 Combine like terms: 0.000009 + -0.000009 = 0.000000 0.000000 + x = -0.00169708 + -0.000009 x = -0.00169708 + -0.000009 Combine like terms: -0.00169708 + -0.000009 = -0.00170608 x = -0.00170608 Simplifying x = -0.00170608

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.00168808, -0.00170608}

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