x^2=(1.70*0.00001)*(0.40-x)

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Solution for x^2=(1.70*0.00001)*(0.40-x) equation:


Simplifying
x2 = (1.70 * 0.00001)(0.40 + -1x)

Multiply 1.70 * 0.00001
x2 = (0.000017)(0.40 + -1x)
x2 = (0.40 * 0.000017 + -1x * 0.000017)
x2 = (0.0000068 + -0.000017x)

Solving
x2 = 0.0000068 + -0.000017x

Solving for variable 'x'.

Reorder the terms:
-0.0000068 + 0.000017x + x2 = 0.0000068 + -0.000017x + -0.0000068 + 0.000017x

Reorder the terms:
-0.0000068 + 0.000017x + x2 = 0.0000068 + -0.0000068 + -0.000017x + 0.000017x

Combine like terms: 0.0000068 + -0.0000068 = 0.0000000
-0.0000068 + 0.000017x + x2 = 0.0000000 + -0.000017x + 0.000017x
-0.0000068 + 0.000017x + x2 = -0.000017x + 0.000017x

Combine like terms: -0.000017x + 0.000017x = 0.000000
-0.0000068 + 0.000017x + x2 = 0.000000

Begin completing the square.

Move the constant term to the right:

Add '0.0000068' to each side of the equation.
-0.0000068 + 0.000017x + 0.0000068 + x2 = 0.000000 + 0.0000068

Reorder the terms:
-0.0000068 + 0.0000068 + 0.000017x + x2 = 0.000000 + 0.0000068

Combine like terms: -0.0000068 + 0.0000068 = 0.0000000
0.0000000 + 0.000017x + x2 = 0.000000 + 0.0000068
0.000017x + x2 = 0.000000 + 0.0000068

Combine like terms: 0.000000 + 0.0000068 = 0.0000068
0.000017x + x2 = 0.0000068

The x term is 0.000017x.  Take half its coefficient (0.0000085).
Square it (0.00000000007225) and add it to both sides.

Add '0.00000000007225' to each side of the equation.
0.000017x + 0.00000000007225 + x2 = 0.0000068 + 0.00000000007225

Reorder the terms:
0.00000000007225 + 0.000017x + x2 = 0.0000068 + 0.00000000007225

Combine like terms: 0.0000068 + 0.00000000007225 = 0.00000680007225
0.00000000007225 + 0.000017x + x2 = 0.00000680007225

Factor a perfect square on the left side:
(x + 0.0000085)(x + 0.0000085) = 0.00000680007225

Calculate the square root of the right side: 0.002607695

Break this problem into two subproblems by setting 
(x + 0.0000085) equal to 0.002607695 and -0.002607695.

Subproblem 1

x + 0.0000085 = 0.002607695 Simplifying x + 0.0000085 = 0.002607695 Reorder the terms: 0.0000085 + x = 0.002607695 Solving 0.0000085 + x = 0.002607695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0000085' to each side of the equation. 0.0000085 + -0.0000085 + x = 0.002607695 + -0.0000085 Combine like terms: 0.0000085 + -0.0000085 = 0.0000000 0.0000000 + x = 0.002607695 + -0.0000085 x = 0.002607695 + -0.0000085 Combine like terms: 0.002607695 + -0.0000085 = 0.002599195 x = 0.002599195 Simplifying x = 0.002599195

Subproblem 2

x + 0.0000085 = -0.002607695 Simplifying x + 0.0000085 = -0.002607695 Reorder the terms: 0.0000085 + x = -0.002607695 Solving 0.0000085 + x = -0.002607695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0000085' to each side of the equation. 0.0000085 + -0.0000085 + x = -0.002607695 + -0.0000085 Combine like terms: 0.0000085 + -0.0000085 = 0.0000000 0.0000000 + x = -0.002607695 + -0.0000085 x = -0.002607695 + -0.0000085 Combine like terms: -0.002607695 + -0.0000085 = -0.002616195 x = -0.002616195 Simplifying x = -0.002616195

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.002599195, -0.002616195}

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