2x(2x-3.4)=8x-6.8

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Solution for 2x(2x-3.4)=8x-6.8 equation:


Simplifying
2x(2x + -3.4) = 8x + -6.8

Reorder the terms:
2x(-3.4 + 2x) = 8x + -6.8
(-3.4 * 2x + 2x * 2x) = 8x + -6.8
(-6.8x + 4x2) = 8x + -6.8

Reorder the terms:
-6.8x + 4x2 = -6.8 + 8x

Solving
-6.8x + 4x2 = -6.8 + 8x

Solving for variable 'x'.

Reorder the terms:
6.8 + -6.8x + -8x + 4x2 = -6.8 + 8x + 6.8 + -8x

Combine like terms: -6.8x + -8x = -14.8x
6.8 + -14.8x + 4x2 = -6.8 + 8x + 6.8 + -8x

Reorder the terms:
6.8 + -14.8x + 4x2 = -6.8 + 6.8 + 8x + -8x

Combine like terms: -6.8 + 6.8 = 0.0
6.8 + -14.8x + 4x2 = 0.0 + 8x + -8x
6.8 + -14.8x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
6.8 + -14.8x + 4x2 = 0

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

Divide each side by '4'.
1.7 + -3.7x + x2 = 0

Move the constant term to the right:

Add '-1.7' to each side of the equation.
1.7 + -3.7x + -1.7 + x2 = 0 + -1.7

Reorder the terms:
1.7 + -1.7 + -3.7x + x2 = 0 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + -3.7x + x2 = 0 + -1.7
-3.7x + x2 = 0 + -1.7

Combine like terms: 0 + -1.7 = -1.7
-3.7x + x2 = -1.7

The x term is -3.7x.  Take half its coefficient (-1.85).
Square it (3.4225) and add it to both sides.

Add '3.4225' to each side of the equation.
-3.7x + 3.4225 + x2 = -1.7 + 3.4225

Reorder the terms:
3.4225 + -3.7x + x2 = -1.7 + 3.4225

Combine like terms: -1.7 + 3.4225 = 1.7225
3.4225 + -3.7x + x2 = 1.7225

Factor a perfect square on the left side:
(x + -1.85)(x + -1.85) = 1.7225

Calculate the square root of the right side: 1.312440475

Break this problem into two subproblems by setting 
(x + -1.85) equal to 1.312440475 and -1.312440475.

Subproblem 1

x + -1.85 = 1.312440475 Simplifying x + -1.85 = 1.312440475 Reorder the terms: -1.85 + x = 1.312440475 Solving -1.85 + x = 1.312440475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.85' to each side of the equation. -1.85 + 1.85 + x = 1.312440475 + 1.85 Combine like terms: -1.85 + 1.85 = 0.00 0.00 + x = 1.312440475 + 1.85 x = 1.312440475 + 1.85 Combine like terms: 1.312440475 + 1.85 = 3.162440475 x = 3.162440475 Simplifying x = 3.162440475

Subproblem 2

x + -1.85 = -1.312440475 Simplifying x + -1.85 = -1.312440475 Reorder the terms: -1.85 + x = -1.312440475 Solving -1.85 + x = -1.312440475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.85' to each side of the equation. -1.85 + 1.85 + x = -1.312440475 + 1.85 Combine like terms: -1.85 + 1.85 = 0.00 0.00 + x = -1.312440475 + 1.85 x = -1.312440475 + 1.85 Combine like terms: -1.312440475 + 1.85 = 0.537559525 x = 0.537559525 Simplifying x = 0.537559525

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.162440475, 0.537559525}

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