x=x^2-11x+24

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Solution for x=x^2-11x+24 equation:


Simplifying
x = x2 + -11x + 24

Reorder the terms:
x = 24 + -11x + x2

Solving
x = 24 + -11x + x2

Solving for variable 'x'.

Reorder the terms:
-24 + x + 11x + -1x2 = 24 + -11x + x2 + -24 + 11x + -1x2

Combine like terms: x + 11x = 12x
-24 + 12x + -1x2 = 24 + -11x + x2 + -24 + 11x + -1x2

Reorder the terms:
-24 + 12x + -1x2 = 24 + -24 + -11x + 11x + x2 + -1x2

Combine like terms: 24 + -24 = 0
-24 + 12x + -1x2 = 0 + -11x + 11x + x2 + -1x2
-24 + 12x + -1x2 = -11x + 11x + x2 + -1x2

Combine like terms: -11x + 11x = 0
-24 + 12x + -1x2 = 0 + x2 + -1x2
-24 + 12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-24 + 12x + -1x2 = 0

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

Divide each side by '-1'.
24 + -12x + x2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -12x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -12x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -12x + x2 = 0 + -24
-12x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-12x + x2 = -24

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 = -24 + 36

Reorder the terms:
36 + -12x + x2 = -24 + 36

Combine like terms: -24 + 36 = 12
36 + -12x + x2 = 12

Factor a perfect square on the left side:
(x + -6)(x + -6) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -6) equal to 3.464101615 and -3.464101615.

Subproblem 1

x + -6 = 3.464101615 Simplifying x + -6 = 3.464101615 Reorder the terms: -6 + x = 3.464101615 Solving -6 + x = 3.464101615 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 = 3.464101615 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.464101615 + 6 x = 3.464101615 + 6 Combine like terms: 3.464101615 + 6 = 9.464101615 x = 9.464101615 Simplifying x = 9.464101615

Subproblem 2

x + -6 = -3.464101615 Simplifying x + -6 = -3.464101615 Reorder the terms: -6 + x = -3.464101615 Solving -6 + x = -3.464101615 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 = -3.464101615 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.464101615 + 6 x = -3.464101615 + 6 Combine like terms: -3.464101615 + 6 = 2.535898385 x = 2.535898385 Simplifying x = 2.535898385

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.464101615, 2.535898385}

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