10x-x^2=11

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Solution for 10x-x^2=11 equation:


Simplifying
10x + -1x2 = 11

Solving
10x + -1x2 = 11

Solving for variable 'x'.

Reorder the terms:
-11 + 10x + -1x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 10x + -1x2 = 0

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

Divide each side by '-1'.
11 + -10x + x2 = 0

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -10x + -11 + x2 = 0 + -11

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

Combine like terms: 11 + -11 = 0
0 + -10x + x2 = 0 + -11
-10x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-10x + x2 = -11

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -11 + 25

Reorder the terms:
25 + -10x + x2 = -11 + 25

Combine like terms: -11 + 25 = 14
25 + -10x + x2 = 14

Factor a perfect square on the left side:
(x + -5)(x + -5) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + -5) equal to 3.741657387 and -3.741657387.

Subproblem 1

x + -5 = 3.741657387 Simplifying x + -5 = 3.741657387 Reorder the terms: -5 + x = 3.741657387 Solving -5 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.741657387 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.741657387 + 5 x = 3.741657387 + 5 Combine like terms: 3.741657387 + 5 = 8.741657387 x = 8.741657387 Simplifying x = 8.741657387

Subproblem 2

x + -5 = -3.741657387 Simplifying x + -5 = -3.741657387 Reorder the terms: -5 + x = -3.741657387 Solving -5 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.741657387 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.741657387 + 5 x = -3.741657387 + 5 Combine like terms: -3.741657387 + 5 = 1.258342613 x = 1.258342613 Simplifying x = 1.258342613

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.741657387, 1.258342613}

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