(-2.5x-20)(x-2)=0

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Solution for (-2.5x-20)(x-2)=0 equation:


Simplifying
(-2.5x + -20)(x + -2) = 0

Reorder the terms:
(-20 + -2.5x)(x + -2) = 0

Reorder the terms:
(-20 + -2.5x)(-2 + x) = 0

Multiply (-20 + -2.5x) * (-2 + x)
(-20(-2 + x) + -2.5x * (-2 + x)) = 0
((-2 * -20 + x * -20) + -2.5x * (-2 + x)) = 0
((40 + -20x) + -2.5x * (-2 + x)) = 0
(40 + -20x + (-2 * -2.5x + x * -2.5x)) = 0
(40 + -20x + (5x + -2.5x2)) = 0

Combine like terms: -20x + 5x = -15x
(40 + -15x + -2.5x2) = 0

Solving
40 + -15x + -2.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2.5 the coefficient of the squared term: 

Divide each side by '-2.5'.
-16 + 6x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 6x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 6x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 6x + x2 = 0 + 16
6x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
6x + x2 = 16

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 16 + 9

Reorder the terms:
9 + 6x + x2 = 16 + 9

Combine like terms: 16 + 9 = 25
9 + 6x + x2 = 25

Factor a perfect square on the left side:
(x + 3)(x + 3) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + 3) equal to 5 and -5.

Subproblem 1

x + 3 = 5 Simplifying x + 3 = 5 Reorder the terms: 3 + x = 5 Solving 3 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5 + -3 x = 5 + -3 Combine like terms: 5 + -3 = 2 x = 2 Simplifying x = 2

Subproblem 2

x + 3 = -5 Simplifying x + 3 = -5 Reorder the terms: 3 + x = -5 Solving 3 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5 + -3 x = -5 + -3 Combine like terms: -5 + -3 = -8 x = -8 Simplifying x = -8

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2, -8}

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