(-12x^2+9x)-(6x^2+10x-1)=

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Solution for (-12x^2+9x)-(6x^2+10x-1)= equation:


Simplifying
(-12x2 + 9x) + -1(6x2 + 10x + -1) = 0

Reorder the terms:
(9x + -12x2) + -1(6x2 + 10x + -1) = 0

Remove parenthesis around (9x + -12x2)
9x + -12x2 + -1(6x2 + 10x + -1) = 0

Reorder the terms:
9x + -12x2 + -1(-1 + 10x + 6x2) = 0
9x + -12x2 + (-1 * -1 + 10x * -1 + 6x2 * -1) = 0
9x + -12x2 + (1 + -10x + -6x2) = 0

Reorder the terms:
1 + 9x + -10x + -12x2 + -6x2 = 0

Combine like terms: 9x + -10x = -1x
1 + -1x + -12x2 + -6x2 = 0

Combine like terms: -12x2 + -6x2 = -18x2
1 + -1x + -18x2 = 0

Solving
1 + -1x + -18x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-18 the coefficient of the squared term: 

Divide each side by '-18'.
-0.05555555556 + 0.05555555556x + x2 = 0

Move the constant term to the right:

Add '0.05555555556' to each side of the equation.
-0.05555555556 + 0.05555555556x + 0.05555555556 + x2 = 0 + 0.05555555556

Reorder the terms:
-0.05555555556 + 0.05555555556 + 0.05555555556x + x2 = 0 + 0.05555555556

Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000
0.00000000000 + 0.05555555556x + x2 = 0 + 0.05555555556
0.05555555556x + x2 = 0 + 0.05555555556

Combine like terms: 0 + 0.05555555556 = 0.05555555556
0.05555555556x + x2 = 0.05555555556

The x term is 0.05555555556x.  Take half its coefficient (0.02777777778).
Square it (0.0007716049384) and add it to both sides.

Add '0.0007716049384' to each side of the equation.
0.05555555556x + 0.0007716049384 + x2 = 0.05555555556 + 0.0007716049384

Reorder the terms:
0.0007716049384 + 0.05555555556x + x2 = 0.05555555556 + 0.0007716049384

Combine like terms: 0.05555555556 + 0.0007716049384 = 0.0563271604984
0.0007716049384 + 0.05555555556x + x2 = 0.0563271604984

Factor a perfect square on the left side:
(x + 0.02777777778)(x + 0.02777777778) = 0.0563271604984

Calculate the square root of the right side: 0.237333437

Break this problem into two subproblems by setting 
(x + 0.02777777778) equal to 0.237333437 and -0.237333437.

Subproblem 1

x + 0.02777777778 = 0.237333437 Simplifying x + 0.02777777778 = 0.237333437 Reorder the terms: 0.02777777778 + x = 0.237333437 Solving 0.02777777778 + x = 0.237333437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02777777778' to each side of the equation. 0.02777777778 + -0.02777777778 + x = 0.237333437 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + x = 0.237333437 + -0.02777777778 x = 0.237333437 + -0.02777777778 Combine like terms: 0.237333437 + -0.02777777778 = 0.20955565922 x = 0.20955565922 Simplifying x = 0.20955565922

Subproblem 2

x + 0.02777777778 = -0.237333437 Simplifying x + 0.02777777778 = -0.237333437 Reorder the terms: 0.02777777778 + x = -0.237333437 Solving 0.02777777778 + x = -0.237333437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02777777778' to each side of the equation. 0.02777777778 + -0.02777777778 + x = -0.237333437 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + x = -0.237333437 + -0.02777777778 x = -0.237333437 + -0.02777777778 Combine like terms: -0.237333437 + -0.02777777778 = -0.26511121478 x = -0.26511121478 Simplifying x = -0.26511121478

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.20955565922, -0.26511121478}

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