7x^2=3-6x

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Solution for 7x^2=3-6x equation:


Simplifying
7x2 = 3 + -6x

Solving
7x2 = 3 + -6x

Solving for variable 'x'.

Reorder the terms:
-3 + 6x + 7x2 = 3 + -6x + -3 + 6x

Reorder the terms:
-3 + 6x + 7x2 = 3 + -3 + -6x + 6x

Combine like terms: 3 + -3 = 0
-3 + 6x + 7x2 = 0 + -6x + 6x
-3 + 6x + 7x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-3 + 6x + 7x2 = 0

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

Divide each side by '7'.
-0.4285714286 + 0.8571428571x + x2 = 0

Move the constant term to the right:

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.8571428571x + 0.4285714286 + x2 = 0 + 0.4285714286

Reorder the terms:
-0.4285714286 + 0.4285714286 + 0.8571428571x + x2 = 0 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + 0.8571428571x + x2 = 0 + 0.4285714286
0.8571428571x + x2 = 0 + 0.4285714286

Combine like terms: 0 + 0.4285714286 = 0.4285714286
0.8571428571x + x2 = 0.4285714286

The x term is 0.8571428571x.  Take half its coefficient (0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
0.8571428571x + 0.1836734694 + x2 = 0.4285714286 + 0.1836734694

Reorder the terms:
0.1836734694 + 0.8571428571x + x2 = 0.4285714286 + 0.1836734694

Combine like terms: 0.4285714286 + 0.1836734694 = 0.612244898
0.1836734694 + 0.8571428571x + x2 = 0.612244898

Factor a perfect square on the left side:
(x + 0.4285714286)(x + 0.4285714286) = 0.612244898

Calculate the square root of the right side: 0.782460796

Break this problem into two subproblems by setting 
(x + 0.4285714286) equal to 0.782460796 and -0.782460796.

Subproblem 1

x + 0.4285714286 = 0.782460796 Simplifying x + 0.4285714286 = 0.782460796 Reorder the terms: 0.4285714286 + x = 0.782460796 Solving 0.4285714286 + x = 0.782460796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = 0.782460796 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 0.782460796 + -0.4285714286 x = 0.782460796 + -0.4285714286 Combine like terms: 0.782460796 + -0.4285714286 = 0.3538893674 x = 0.3538893674 Simplifying x = 0.3538893674

Subproblem 2

x + 0.4285714286 = -0.782460796 Simplifying x + 0.4285714286 = -0.782460796 Reorder the terms: 0.4285714286 + x = -0.782460796 Solving 0.4285714286 + x = -0.782460796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = -0.782460796 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -0.782460796 + -0.4285714286 x = -0.782460796 + -0.4285714286 Combine like terms: -0.782460796 + -0.4285714286 = -1.2110322246 x = -1.2110322246 Simplifying x = -1.2110322246

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.3538893674, -1.2110322246}

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