-8.3(x+2)(x-9)=0

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Solution for -8.3(x+2)(x-9)=0 equation:


Simplifying
-8.3(x + 2)(x + -9) = 0

Reorder the terms:
-8.3(2 + x)(x + -9) = 0

Reorder the terms:
-8.3(2 + x)(-9 + x) = 0

Multiply (2 + x) * (-9 + x)
-8.3(2(-9 + x) + x(-9 + x)) = 0
-8.3((-9 * 2 + x * 2) + x(-9 + x)) = 0
-8.3((-18 + 2x) + x(-9 + x)) = 0
-8.3(-18 + 2x + (-9 * x + x * x)) = 0
-8.3(-18 + 2x + (-9x + x2)) = 0

Combine like terms: 2x + -9x = -7x
-8.3(-18 + -7x + x2) = 0
(-18 * -8.3 + -7x * -8.3 + x2 * -8.3) = 0
(149.4 + 58.1x + -8.3x2) = 0

Solving
149.4 + 58.1x + -8.3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-8.3 the coefficient of the squared term: 

Divide each side by '-8.3'.
-18 + -7x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -7x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -7x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -7x + x2 = 0 + 18
-7x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-7x + x2 = 18

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 = 18 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 18 + 12.25

Combine like terms: 18 + 12.25 = 30.25
12.25 + -7x + x2 = 30.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 30.25

Calculate the square root of the right side: 5.5

Break this problem into two subproblems by setting 
(x + -3.5) equal to 5.5 and -5.5.

Subproblem 1

x + -3.5 = 5.5 Simplifying x + -3.5 = 5.5 Reorder the terms: -3.5 + x = 5.5 Solving -3.5 + x = 5.5 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 = 5.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.5 + 3.5 x = 5.5 + 3.5 Combine like terms: 5.5 + 3.5 = 9 x = 9 Simplifying x = 9

Subproblem 2

x + -3.5 = -5.5 Simplifying x + -3.5 = -5.5 Reorder the terms: -3.5 + x = -5.5 Solving -3.5 + x = -5.5 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 = -5.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.5 + 3.5 x = -5.5 + 3.5 Combine like terms: -5.5 + 3.5 = -2 x = -2 Simplifying x = -2

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9, -2}

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