x(x-21)=18

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Solution for x(x-21)=18 equation:


Simplifying
x(x + -21) = 18

Reorder the terms:
x(-21 + x) = 18
(-21 * x + x * x) = 18
(-21x + x2) = 18

Solving
-21x + x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + -21x + x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + -21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -21x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -21x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -21x + x2 = 0 + 18
-21x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-21x + x2 = 18

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 = 18 + 110.25

Reorder the terms:
110.25 + -21x + x2 = 18 + 110.25

Combine like terms: 18 + 110.25 = 128.25
110.25 + -21x + x2 = 128.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 128.25

Calculate the square root of the right side: 11.324751653

Break this problem into two subproblems by setting 
(x + -10.5) equal to 11.324751653 and -11.324751653.

Subproblem 1

x + -10.5 = 11.324751653 Simplifying x + -10.5 = 11.324751653 Reorder the terms: -10.5 + x = 11.324751653 Solving -10.5 + x = 11.324751653 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 = 11.324751653 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 11.324751653 + 10.5 x = 11.324751653 + 10.5 Combine like terms: 11.324751653 + 10.5 = 21.824751653 x = 21.824751653 Simplifying x = 21.824751653

Subproblem 2

x + -10.5 = -11.324751653 Simplifying x + -10.5 = -11.324751653 Reorder the terms: -10.5 + x = -11.324751653 Solving -10.5 + x = -11.324751653 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 = -11.324751653 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -11.324751653 + 10.5 x = -11.324751653 + 10.5 Combine like terms: -11.324751653 + 10.5 = -0.824751653 x = -0.824751653 Simplifying x = -0.824751653

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21.824751653, -0.824751653}

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