1320=x(x-3)

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Solution for 1320=x(x-3) equation:


Simplifying
1320 = x(x + -3)

Reorder the terms:
1320 = x(-3 + x)
1320 = (-3 * x + x * x)
1320 = (-3x + x2)

Solving
1320 = -3x + x2

Solving for variable 'x'.

Reorder the terms:
1320 + 3x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
1320 + 3x + -1x2 = 0 + x2 + -1x2
1320 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1320 + 3x + -1x2 = 0

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

Divide each side by '-1'.
-1320 + -3x + x2 = 0

Move the constant term to the right:

Add '1320' to each side of the equation.
-1320 + -3x + 1320 + x2 = 0 + 1320

Reorder the terms:
-1320 + 1320 + -3x + x2 = 0 + 1320

Combine like terms: -1320 + 1320 = 0
0 + -3x + x2 = 0 + 1320
-3x + x2 = 0 + 1320

Combine like terms: 0 + 1320 = 1320
-3x + x2 = 1320

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 1320 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 1320 + 2.25

Combine like terms: 1320 + 2.25 = 1322.25
2.25 + -3x + x2 = 1322.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1322.25

Calculate the square root of the right side: 36.362755671

Break this problem into two subproblems by setting 
(x + -1.5) equal to 36.362755671 and -36.362755671.

Subproblem 1

x + -1.5 = 36.362755671 Simplifying x + -1.5 = 36.362755671 Reorder the terms: -1.5 + x = 36.362755671 Solving -1.5 + x = 36.362755671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 36.362755671 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 36.362755671 + 1.5 x = 36.362755671 + 1.5 Combine like terms: 36.362755671 + 1.5 = 37.862755671 x = 37.862755671 Simplifying x = 37.862755671

Subproblem 2

x + -1.5 = -36.362755671 Simplifying x + -1.5 = -36.362755671 Reorder the terms: -1.5 + x = -36.362755671 Solving -1.5 + x = -36.362755671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -36.362755671 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -36.362755671 + 1.5 x = -36.362755671 + 1.5 Combine like terms: -36.362755671 + 1.5 = -34.862755671 x = -34.862755671 Simplifying x = -34.862755671

Solution

The solution to the problem is based on the solutions from the subproblems. x = {37.862755671, -34.862755671}

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