3x^2+4x=2x^2+3

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Solution for 3x^2+4x=2x^2+3 equation:


Simplifying
3x2 + 4x = 2x2 + 3

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

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

Solving
4x + 3x2 = 3 + 2x2

Solving for variable 'x'.

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

Combine like terms: 3x2 + -2x2 = 1x2
-3 + 4x + 1x2 = 3 + 2x2 + -3 + -2x2

Reorder the terms:
-3 + 4x + 1x2 = 3 + -3 + 2x2 + -2x2

Combine like terms: 3 + -3 = 0
-3 + 4x + 1x2 = 0 + 2x2 + -2x2
-3 + 4x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-3 + 4x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 4x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 4x + x2 = 0 + 3

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

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

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 3 + 4

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

Combine like terms: 3 + 4 = 7
4 + 4x + x2 = 7

Factor a perfect square on the left side:
(x + 2)(x + 2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 2) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + 2 = 2.645751311 Simplifying x + 2 = 2.645751311 Reorder the terms: 2 + x = 2.645751311 Solving 2 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.645751311 + -2 x = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 x = 0.645751311 Simplifying x = 0.645751311

Subproblem 2

x + 2 = -2.645751311 Simplifying x + 2 = -2.645751311 Reorder the terms: 2 + x = -2.645751311 Solving 2 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.645751311 + -2 x = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 x = -4.645751311 Simplifying x = -4.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.645751311, -4.645751311}

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