10x^2+5-6x-9x^2-11x=

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Solution for 10x^2+5-6x-9x^2-11x= equation:


Simplifying
10x2 + 5 + -6x + -9x2 + -11x = 0

Reorder the terms:
5 + -6x + -11x + 10x2 + -9x2 = 0

Combine like terms: -6x + -11x = -17x
5 + -17x + 10x2 + -9x2 = 0

Combine like terms: 10x2 + -9x2 = 1x2
5 + -17x + 1x2 = 0

Solving
5 + -17x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -17x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -17x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -17x + x2 = 0 + -5
-17x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-17x + x2 = -5

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = -5 + 72.25

Reorder the terms:
72.25 + -17x + x2 = -5 + 72.25

Combine like terms: -5 + 72.25 = 67.25
72.25 + -17x + x2 = 67.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 67.25

Calculate the square root of the right side: 8.200609733

Break this problem into two subproblems by setting 
(x + -8.5) equal to 8.200609733 and -8.200609733.

Subproblem 1

x + -8.5 = 8.200609733 Simplifying x + -8.5 = 8.200609733 Reorder the terms: -8.5 + x = 8.200609733 Solving -8.5 + x = 8.200609733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 8.200609733 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.200609733 + 8.5 x = 8.200609733 + 8.5 Combine like terms: 8.200609733 + 8.5 = 16.700609733 x = 16.700609733 Simplifying x = 16.700609733

Subproblem 2

x + -8.5 = -8.200609733 Simplifying x + -8.5 = -8.200609733 Reorder the terms: -8.5 + x = -8.200609733 Solving -8.5 + x = -8.200609733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -8.200609733 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.200609733 + 8.5 x = -8.200609733 + 8.5 Combine like terms: -8.200609733 + 8.5 = 0.299390267 x = 0.299390267 Simplifying x = 0.299390267

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.700609733, 0.299390267}

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