x^2+11x-21=0

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Solution for x^2+11x-21=0 equation:


Simplifying
x2 + 11x + -21 = 0

Reorder the terms:
-21 + 11x + x2 = 0

Solving
-21 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 11x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 11x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 11x + x2 = 0 + 21
11x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
11x + x2 = 21

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 21 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 21 + 30.25

Combine like terms: 21 + 30.25 = 51.25
30.25 + 11x + x2 = 51.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(x + 5.5) equal to 7.158910532 and -7.158910532.

Subproblem 1

x + 5.5 = 7.158910532 Simplifying x + 5.5 = 7.158910532 Reorder the terms: 5.5 + x = 7.158910532 Solving 5.5 + x = 7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 7.158910532 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 7.158910532 + -5.5 x = 7.158910532 + -5.5 Combine like terms: 7.158910532 + -5.5 = 1.658910532 x = 1.658910532 Simplifying x = 1.658910532

Subproblem 2

x + 5.5 = -7.158910532 Simplifying x + 5.5 = -7.158910532 Reorder the terms: 5.5 + x = -7.158910532 Solving 5.5 + x = -7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -7.158910532 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -7.158910532 + -5.5 x = -7.158910532 + -5.5 Combine like terms: -7.158910532 + -5.5 = -12.658910532 x = -12.658910532 Simplifying x = -12.658910532

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.658910532, -12.658910532}

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