x^2-21x-36=0

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Solution for x^2-21x-36=0 equation:


Simplifying
x2 + -21x + -36 = 0

Reorder the terms:
-36 + -21x + x2 = 0

Solving
-36 + -21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -21x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -21x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -21x + x2 = 0 + 36
-21x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-21x + x2 = 36

The x term is -21x.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21x + 110.25 + x2 = 36 + 110.25

Reorder the terms:
110.25 + -21x + x2 = 36 + 110.25

Combine like terms: 36 + 110.25 = 146.25
110.25 + -21x + x2 = 146.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 146.25

Calculate the square root of the right side: 12.093386622

Break this problem into two subproblems by setting 
(x + -10.5) equal to 12.093386622 and -12.093386622.

Subproblem 1

x + -10.5 = 12.093386622 Simplifying x + -10.5 = 12.093386622 Reorder the terms: -10.5 + x = 12.093386622 Solving -10.5 + x = 12.093386622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 12.093386622 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 12.093386622 + 10.5 x = 12.093386622 + 10.5 Combine like terms: 12.093386622 + 10.5 = 22.593386622 x = 22.593386622 Simplifying x = 22.593386622

Subproblem 2

x + -10.5 = -12.093386622 Simplifying x + -10.5 = -12.093386622 Reorder the terms: -10.5 + x = -12.093386622 Solving -10.5 + x = -12.093386622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -12.093386622 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -12.093386622 + 10.5 x = -12.093386622 + 10.5 Combine like terms: -12.093386622 + 10.5 = -1.593386622 x = -1.593386622 Simplifying x = -1.593386622

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.593386622, -1.593386622}

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