9x=x^2-6

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Solution for 9x=x^2-6 equation:


Simplifying
9x = x2 + -6

Reorder the terms:
9x = -6 + x2

Solving
9x = -6 + x2

Solving for variable 'x'.

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

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

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

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

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

Divide each side by '-1'.
-6 + -9x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -9x + 6 + x2 = 0 + 6

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

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

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

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 6 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 6 + 20.25

Combine like terms: 6 + 20.25 = 26.25
20.25 + -9x + x2 = 26.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + -4.5) equal to 5.123475383 and -5.123475383.

Subproblem 1

x + -4.5 = 5.123475383 Simplifying x + -4.5 = 5.123475383 Reorder the terms: -4.5 + x = 5.123475383 Solving -4.5 + x = 5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.123475383 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.123475383 + 4.5 x = 5.123475383 + 4.5 Combine like terms: 5.123475383 + 4.5 = 9.623475383 x = 9.623475383 Simplifying x = 9.623475383

Subproblem 2

x + -4.5 = -5.123475383 Simplifying x + -4.5 = -5.123475383 Reorder the terms: -4.5 + x = -5.123475383 Solving -4.5 + x = -5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.123475383 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.123475383 + 4.5 x = -5.123475383 + 4.5 Combine like terms: -5.123475383 + 4.5 = -0.623475383 x = -0.623475383 Simplifying x = -0.623475383

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.623475383, -0.623475383}

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