23=2x(x+3)

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Solution for 23=2x(x+3) equation:


Simplifying
23 = 2x(x + 3)

Reorder the terms:
23 = 2x(3 + x)
23 = (3 * 2x + x * 2x)
23 = (6x + 2x2)

Solving
23 = 6x + 2x2

Solving for variable 'x'.

Reorder the terms:
23 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
23 + -6x + -2x2 = 0 + 2x2 + -2x2
23 + -6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
23 + -6x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-11.5 + 3x + x2 = 0

Move the constant term to the right:

Add '11.5' to each side of the equation.
-11.5 + 3x + 11.5 + x2 = 0 + 11.5

Reorder the terms:
-11.5 + 11.5 + 3x + x2 = 0 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + 3x + x2 = 0 + 11.5
3x + x2 = 0 + 11.5

Combine like terms: 0 + 11.5 = 11.5
3x + x2 = 11.5

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 = 11.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 11.5 + 2.25

Combine like terms: 11.5 + 2.25 = 13.75
2.25 + 3x + x2 = 13.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 13.75

Calculate the square root of the right side: 3.708099244

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.708099244 and -3.708099244.

Subproblem 1

x + 1.5 = 3.708099244 Simplifying x + 1.5 = 3.708099244 Reorder the terms: 1.5 + x = 3.708099244 Solving 1.5 + x = 3.708099244 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 = 3.708099244 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.708099244 + -1.5 x = 3.708099244 + -1.5 Combine like terms: 3.708099244 + -1.5 = 2.208099244 x = 2.208099244 Simplifying x = 2.208099244

Subproblem 2

x + 1.5 = -3.708099244 Simplifying x + 1.5 = -3.708099244 Reorder the terms: 1.5 + x = -3.708099244 Solving 1.5 + x = -3.708099244 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 = -3.708099244 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.708099244 + -1.5 x = -3.708099244 + -1.5 Combine like terms: -3.708099244 + -1.5 = -5.208099244 x = -5.208099244 Simplifying x = -5.208099244

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.208099244, -5.208099244}

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