x*x+10x-21=0

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Solution for x*x+10x-21=0 equation:


Simplifying
x * x + 10x + -21 = 0

Multiply x * x
x2 + 10x + -21 = 0

Reorder the terms:
-21 + 10x + x2 = 0

Solving
-21 + 10x + 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 + 10x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 10x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 10x + x2 = 0 + 21
10x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
10x + x2 = 21

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 = 21 + 25

Reorder the terms:
25 + 10x + x2 = 21 + 25

Combine like terms: 21 + 25 = 46
25 + 10x + x2 = 46

Factor a perfect square on the left side:
(x + 5)(x + 5) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + 5) equal to 6.782329983 and -6.782329983.


Subproblem 1
x + 5 = 6.782329983

Simplifying
x + 5 = 6.782329983

Reorder the terms:
5 + x = 6.782329983

Solving
5 + x = 6.782329983

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 = 6.782329983 + -5

Combine like terms: 5 + -5 = 0
0 + x = 6.782329983 + -5
x = 6.782329983 + -5

Combine like terms: 6.782329983 + -5 = 1.782329983
x = 1.782329983

Simplifying
x = 1.782329983


Subproblem 2
x + 5 = -6.782329983

Simplifying
x + 5 = -6.782329983

Reorder the terms:
5 + x = -6.782329983

Solving
5 + x = -6.782329983

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 = -6.782329983 + -5

Combine like terms: 5 + -5 = 0
0 + x = -6.782329983 + -5
x = -6.782329983 + -5

Combine like terms: -6.782329983 + -5 = -11.782329983
x = -11.782329983

Simplifying
x = -11.782329983


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.782329983, -11.782329983}

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