x^2-4=2x^2-12x+18

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Solution for x^2-4=2x^2-12x+18 equation:


Simplifying
x2 + -4 = 2x2 + -12x + 18

Reorder the terms:
-4 + x2 = 2x2 + -12x + 18

Reorder the terms:
-4 + x2 = 18 + -12x + 2x2

Solving
-4 + x2 = 18 + -12x + 2x2

Solving for variable 'x'.

Reorder the terms:
-4 + -18 + 12x + x2 + -2x2 = 18 + -12x + 2x2 + -18 + 12x + -2x2

Combine like terms: -4 + -18 = -22
-22 + 12x + x2 + -2x2 = 18 + -12x + 2x2 + -18 + 12x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-22 + 12x + -1x2 = 18 + -12x + 2x2 + -18 + 12x + -2x2

Reorder the terms:
-22 + 12x + -1x2 = 18 + -18 + -12x + 12x + 2x2 + -2x2

Combine like terms: 18 + -18 = 0
-22 + 12x + -1x2 = 0 + -12x + 12x + 2x2 + -2x2
-22 + 12x + -1x2 = -12x + 12x + 2x2 + -2x2

Combine like terms: -12x + 12x = 0
-22 + 12x + -1x2 = 0 + 2x2 + -2x2
-22 + 12x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-22 + 12x + -1x2 = 0

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

Divide each side by '-1'.
22 + -12x + x2 = 0

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + -12x + -22 + x2 = 0 + -22

Reorder the terms:
22 + -22 + -12x + x2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -12x + x2 = 0 + -22
-12x + x2 = 0 + -22

Combine like terms: 0 + -22 = -22
-12x + x2 = -22

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -22 + 36

Reorder the terms:
36 + -12x + x2 = -22 + 36

Combine like terms: -22 + 36 = 14
36 + -12x + x2 = 14

Factor a perfect square on the left side:
(x + -6)(x + -6) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + -6) equal to 3.741657387 and -3.741657387.

Subproblem 1

x + -6 = 3.741657387 Simplifying x + -6 = 3.741657387 Reorder the terms: -6 + x = 3.741657387 Solving -6 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 3.741657387 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.741657387 + 6 x = 3.741657387 + 6 Combine like terms: 3.741657387 + 6 = 9.741657387 x = 9.741657387 Simplifying x = 9.741657387

Subproblem 2

x + -6 = -3.741657387 Simplifying x + -6 = -3.741657387 Reorder the terms: -6 + x = -3.741657387 Solving -6 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -3.741657387 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.741657387 + 6 x = -3.741657387 + 6 Combine like terms: -3.741657387 + 6 = 2.258342613 x = 2.258342613 Simplifying x = 2.258342613

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.741657387, 2.258342613}

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