130=((.5)(x+-7))(x)

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Solution for 130=((.5)(x+-7))(x) equation:


Simplifying
130 = ((0.5)(x + -7))(x)

Reorder the terms:
130 = (0.5(-7 + x))(x)
130 = ((-7 * 0.5 + x * 0.5))(x)
130 = ((-3.5 + 0.5x))(x)

Reorder the terms for easier multiplication:
130 = x(-3.5 + 0.5x)
130 = (-3.5 * x + 0.5x * x)
130 = (-3.5x + 0.5x2)

Solving
130 = -3.5x + 0.5x2

Solving for variable 'x'.

Reorder the terms:
130 + 3.5x + -0.5x2 = -3.5x + 3.5x + 0.5x2 + -0.5x2

Combine like terms: -3.5x + 3.5x = 0.0
130 + 3.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2
130 + 3.5x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
130 + 3.5x + -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'.
-260 + -7x + x2 = 0

Move the constant term to the right:

Add '260' to each side of the equation.
-260 + -7x + 260 + x2 = 0 + 260

Reorder the terms:
-260 + 260 + -7x + x2 = 0 + 260

Combine like terms: -260 + 260 = 0
0 + -7x + x2 = 0 + 260
-7x + x2 = 0 + 260

Combine like terms: 0 + 260 = 260
-7x + x2 = 260

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 260 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 260 + 12.25

Combine like terms: 260 + 12.25 = 272.25
12.25 + -7x + x2 = 272.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 272.25

Calculate the square root of the right side: 16.5

Break this problem into two subproblems by setting 
(x + -3.5) equal to 16.5 and -16.5.

Subproblem 1

x + -3.5 = 16.5 Simplifying x + -3.5 = 16.5 Reorder the terms: -3.5 + x = 16.5 Solving -3.5 + x = 16.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 16.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 16.5 + 3.5 x = 16.5 + 3.5 Combine like terms: 16.5 + 3.5 = 20 x = 20 Simplifying x = 20

Subproblem 2

x + -3.5 = -16.5 Simplifying x + -3.5 = -16.5 Reorder the terms: -3.5 + x = -16.5 Solving -3.5 + x = -16.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -16.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -16.5 + 3.5 x = -16.5 + 3.5 Combine like terms: -16.5 + 3.5 = -13 x = -13 Simplifying x = -13

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20, -13}

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