.5x-.1x(18-5x)=-.3(x-7)

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Solution for .5x-.1x(18-5x)=-.3(x-7) equation:


Simplifying
0.5x + -0.1x(18 + -5x) = -0.3(x + -7)
0.5x + (18 * -0.1x + -5x * -0.1x) = -0.3(x + -7)
0.5x + (-1.8x + 0.5x2) = -0.3(x + -7)

Combine like terms: 0.5x + -1.8x = -1.3x
-1.3x + 0.5x2 = -0.3(x + -7)

Reorder the terms:
-1.3x + 0.5x2 = -0.3(-7 + x)
-1.3x + 0.5x2 = (-7 * -0.3 + x * -0.3)
-1.3x + 0.5x2 = (2.1 + -0.3x)

Solving
-1.3x + 0.5x2 = 2.1 + -0.3x

Solving for variable 'x'.

Reorder the terms:
-2.1 + -1.3x + 0.3x + 0.5x2 = 2.1 + -0.3x + -2.1 + 0.3x

Combine like terms: -1.3x + 0.3x = -1x
-2.1 + -1x + 0.5x2 = 2.1 + -0.3x + -2.1 + 0.3x

Reorder the terms:
-2.1 + -1x + 0.5x2 = 2.1 + -2.1 + -0.3x + 0.3x

Combine like terms: 2.1 + -2.1 = 0.0
-2.1 + -1x + 0.5x2 = 0.0 + -0.3x + 0.3x
-2.1 + -1x + 0.5x2 = -0.3x + 0.3x

Combine like terms: -0.3x + 0.3x = 0.0
-2.1 + -1x + 0.5x2 = 0.0

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

Divide each side by '0.5'.
-4.2 + -2x + x2 = 0

Move the constant term to the right:

Add '4.2' to each side of the equation.
-4.2 + -2x + 4.2 + x2 = 0 + 4.2

Reorder the terms:
-4.2 + 4.2 + -2x + x2 = 0 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + -2x + x2 = 0 + 4.2
-2x + x2 = 0 + 4.2

Combine like terms: 0 + 4.2 = 4.2
-2x + x2 = 4.2

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 4.2 + 1

Reorder the terms:
1 + -2x + x2 = 4.2 + 1

Combine like terms: 4.2 + 1 = 5.2
1 + -2x + x2 = 5.2

Factor a perfect square on the left side:
(x + -1)(x + -1) = 5.2

Calculate the square root of the right side: 2.28035085

Break this problem into two subproblems by setting 
(x + -1) equal to 2.28035085 and -2.28035085.

Subproblem 1

x + -1 = 2.28035085 Simplifying x + -1 = 2.28035085 Reorder the terms: -1 + x = 2.28035085 Solving -1 + x = 2.28035085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.28035085 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.28035085 + 1 x = 2.28035085 + 1 Combine like terms: 2.28035085 + 1 = 3.28035085 x = 3.28035085 Simplifying x = 3.28035085

Subproblem 2

x + -1 = -2.28035085 Simplifying x + -1 = -2.28035085 Reorder the terms: -1 + x = -2.28035085 Solving -1 + x = -2.28035085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.28035085 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.28035085 + 1 x = -2.28035085 + 1 Combine like terms: -2.28035085 + 1 = -1.28035085 x = -1.28035085 Simplifying x = -1.28035085

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.28035085, -1.28035085}

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