4x*x+3=6+2x

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Solution for 4x*x+3=6+2x equation:


Simplifying
4x * x + 3 = 6 + 2x

Multiply x * x
4x2 + 3 = 6 + 2x

Reorder the terms:
3 + 4x2 = 6 + 2x

Solving
3 + 4x2 = 6 + 2x

Solving for variable 'x'.

Reorder the terms:
3 + -6 + -2x + 4x2 = 6 + 2x + -6 + -2x

Combine like terms: 3 + -6 = -3
-3 + -2x + 4x2 = 6 + 2x + -6 + -2x

Reorder the terms:
-3 + -2x + 4x2 = 6 + -6 + 2x + -2x

Combine like terms: 6 + -6 = 0
-3 + -2x + 4x2 = 0 + 2x + -2x
-3 + -2x + 4x2 = 2x + -2x

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

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

Divide each side by '4'.
-0.75 + -0.5x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -0.5x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -0.5x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -0.5x + x2 = 0 + 0.75
-0.5x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-0.5x + x2 = 0.75

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.75 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.75 + 0.0625

Combine like terms: 0.75 + 0.0625 = 0.8125
0.0625 + -0.5x + x2 = 0.8125

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.8125

Calculate the square root of the right side: 0.901387819

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.901387819 and -0.901387819.

Subproblem 1

x + -0.25 = 0.901387819 Simplifying x + -0.25 = 0.901387819 Reorder the terms: -0.25 + x = 0.901387819 Solving -0.25 + x = 0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.901387819 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.901387819 + 0.25 x = 0.901387819 + 0.25 Combine like terms: 0.901387819 + 0.25 = 1.151387819 x = 1.151387819 Simplifying x = 1.151387819

Subproblem 2

x + -0.25 = -0.901387819 Simplifying x + -0.25 = -0.901387819 Reorder the terms: -0.25 + x = -0.901387819 Solving -0.25 + x = -0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.901387819 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.901387819 + 0.25 x = -0.901387819 + 0.25 Combine like terms: -0.901387819 + 0.25 = -0.651387819 x = -0.651387819 Simplifying x = -0.651387819

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.151387819, -0.651387819}

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