8x^2+32-9x^2=5x

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Solution for 8x^2+32-9x^2=5x equation:


Simplifying
8x2 + 32 + -9x2 = 5x

Reorder the terms:
32 + 8x2 + -9x2 = 5x

Combine like terms: 8x2 + -9x2 = -1x2
32 + -1x2 = 5x

Solving
32 + -1x2 = 5x

Solving for variable 'x'.

Reorder the terms:
32 + -5x + -1x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
32 + -5x + -1x2 = 0

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

Divide each side by '-1'.
-32 + 5x + x2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 5x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 5x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 5x + x2 = 0 + 32
5x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
5x + x2 = 32

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 32 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 32 + 6.25

Combine like terms: 32 + 6.25 = 38.25
6.25 + 5x + x2 = 38.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(x + 2.5) equal to 6.184658438 and -6.184658438.

Subproblem 1

x + 2.5 = 6.184658438 Simplifying x + 2.5 = 6.184658438 Reorder the terms: 2.5 + x = 6.184658438 Solving 2.5 + x = 6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 6.184658438 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.184658438 + -2.5 x = 6.184658438 + -2.5 Combine like terms: 6.184658438 + -2.5 = 3.684658438 x = 3.684658438 Simplifying x = 3.684658438

Subproblem 2

x + 2.5 = -6.184658438 Simplifying x + 2.5 = -6.184658438 Reorder the terms: 2.5 + x = -6.184658438 Solving 2.5 + x = -6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -6.184658438 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.184658438 + -2.5 x = -6.184658438 + -2.5 Combine like terms: -6.184658438 + -2.5 = -8.684658438 x = -8.684658438 Simplifying x = -8.684658438

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.684658438, -8.684658438}

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