2x(x+2)=3

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


Simplifying
2x(x + 2) = 3

Reorder the terms:
2x(2 + x) = 3
(2 * 2x + x * 2x) = 3
(4x + 2x2) = 3

Solving
4x + 2x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 4x + 2x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 4x + 2x2 = 0

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

Divide each side by '2'.
-1.5 + 2x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 2x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 2x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 2x + x2 = 0 + 1.5
2x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
2x + x2 = 1.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 1.5 + 1

Reorder the terms:
1 + 2x + x2 = 1.5 + 1

Combine like terms: 1.5 + 1 = 2.5
1 + 2x + x2 = 2.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(x + 1) equal to 1.58113883 and -1.58113883.

Subproblem 1

x + 1 = 1.58113883 Simplifying x + 1 = 1.58113883 Reorder the terms: 1 + x = 1.58113883 Solving 1 + x = 1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.58113883 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.58113883 + -1 x = 1.58113883 + -1 Combine like terms: 1.58113883 + -1 = 0.58113883 x = 0.58113883 Simplifying x = 0.58113883

Subproblem 2

x + 1 = -1.58113883 Simplifying x + 1 = -1.58113883 Reorder the terms: 1 + x = -1.58113883 Solving 1 + x = -1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.58113883 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.58113883 + -1 x = -1.58113883 + -1 Combine like terms: -1.58113883 + -1 = -2.58113883 x = -2.58113883 Simplifying x = -2.58113883

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.58113883, -2.58113883}

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