6x-x^2+4=0

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Solution for 6x-x^2+4=0 equation:


Simplifying
6x + -1x2 + 4 = 0

Reorder the terms:
4 + 6x + -1x2 = 0

Solving
4 + 6x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
-4 + -6x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -6x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -6x + x2 = 0 + 4

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

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

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 4 + 9

Reorder the terms:
9 + -6x + x2 = 4 + 9

Combine like terms: 4 + 9 = 13
9 + -6x + x2 = 13

Factor a perfect square on the left side:
(x + -3)(x + -3) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -3) equal to 3.605551275 and -3.605551275.

Subproblem 1

x + -3 = 3.605551275 Simplifying x + -3 = 3.605551275 Reorder the terms: -3 + x = 3.605551275 Solving -3 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.605551275 + 3 x = 3.605551275 + 3 Combine like terms: 3.605551275 + 3 = 6.605551275 x = 6.605551275 Simplifying x = 6.605551275

Subproblem 2

x + -3 = -3.605551275 Simplifying x + -3 = -3.605551275 Reorder the terms: -3 + x = -3.605551275 Solving -3 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.605551275 + 3 x = -3.605551275 + 3 Combine like terms: -3.605551275 + 3 = -0.605551275 x = -0.605551275 Simplifying x = -0.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.605551275, -0.605551275}

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