3.5=(0.1-x)(0.15-x)

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Solution for 3.5=(0.1-x)(0.15-x) equation:


Simplifying
3.5 = (0.1 + -1x)(0.15 + -1x)

Multiply (0.1 + -1x) * (0.15 + -1x)
3.5 = (0.1(0.15 + -1x) + -1x * (0.15 + -1x))
3.5 = ((0.15 * 0.1 + -1x * 0.1) + -1x * (0.15 + -1x))
3.5 = ((0.015 + -0.1x) + -1x * (0.15 + -1x))
3.5 = (0.015 + -0.1x + (0.15 * -1x + -1x * -1x))
3.5 = (0.015 + -0.1x + (-0.15x + 1x2))

Combine like terms: -0.1x + -0.15x = -0.25x
3.5 = (0.015 + -0.25x + 1x2)

Solving
3.5 = 0.015 + -0.25x + 1x2

Solving for variable 'x'.

Combine like terms: 3.5 + -0.015 = 3.485
3.485 + 0.25x + -1x2 = 0.015 + -0.25x + 1x2 + -0.015 + 0.25x + -1x2

Reorder the terms:
3.485 + 0.25x + -1x2 = 0.015 + -0.015 + -0.25x + 0.25x + 1x2 + -1x2

Combine like terms: 0.015 + -0.015 = 0.000
3.485 + 0.25x + -1x2 = 0.000 + -0.25x + 0.25x + 1x2 + -1x2
3.485 + 0.25x + -1x2 = -0.25x + 0.25x + 1x2 + -1x2

Combine like terms: -0.25x + 0.25x = 0.00
3.485 + 0.25x + -1x2 = 0.00 + 1x2 + -1x2
3.485 + 0.25x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
3.485 + 0.25x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3.485 + -0.25x + x2 = 0

Move the constant term to the right:

Add '3.485' to each side of the equation.
-3.485 + -0.25x + 3.485 + x2 = 0 + 3.485

Reorder the terms:
-3.485 + 3.485 + -0.25x + x2 = 0 + 3.485

Combine like terms: -3.485 + 3.485 = 0.000
0.000 + -0.25x + x2 = 0 + 3.485
-0.25x + x2 = 0 + 3.485

Combine like terms: 0 + 3.485 = 3.485
-0.25x + x2 = 3.485

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 3.485 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 3.485 + 0.015625

Combine like terms: 3.485 + 0.015625 = 3.500625
0.015625 + -0.25x + x2 = 3.500625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 3.500625

Calculate the square root of the right side: 1.870995724

Break this problem into two subproblems by setting 
(x + -0.125) equal to 1.870995724 and -1.870995724.

Subproblem 1

x + -0.125 = 1.870995724 Simplifying x + -0.125 = 1.870995724 Reorder the terms: -0.125 + x = 1.870995724 Solving -0.125 + x = 1.870995724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 1.870995724 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 1.870995724 + 0.125 x = 1.870995724 + 0.125 Combine like terms: 1.870995724 + 0.125 = 1.995995724 x = 1.995995724 Simplifying x = 1.995995724

Subproblem 2

x + -0.125 = -1.870995724 Simplifying x + -0.125 = -1.870995724 Reorder the terms: -0.125 + x = -1.870995724 Solving -0.125 + x = -1.870995724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -1.870995724 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -1.870995724 + 0.125 x = -1.870995724 + 0.125 Combine like terms: -1.870995724 + 0.125 = -1.745995724 x = -1.745995724 Simplifying x = -1.745995724

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.995995724, -1.745995724}

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