(7x-1)*(0.4x-4)=0

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Solution for (7x-1)*(0.4x-4)=0 equation:


Simplifying
(7x + -1)(0.4x + -4) = 0

Reorder the terms:
(-1 + 7x)(0.4x + -4) = 0

Reorder the terms:
(-1 + 7x)(-4 + 0.4x) = 0

Multiply (-1 + 7x) * (-4 + 0.4x)
(-1(-4 + 0.4x) + 7x * (-4 + 0.4x)) = 0
((-4 * -1 + 0.4x * -1) + 7x * (-4 + 0.4x)) = 0
((4 + -0.4x) + 7x * (-4 + 0.4x)) = 0
(4 + -0.4x + (-4 * 7x + 0.4x * 7x)) = 0
(4 + -0.4x + (-28x + 2.8x2)) = 0

Combine like terms: -0.4x + -28x = -28.4x
(4 + -28.4x + 2.8x2) = 0

Solving
4 + -28.4x + 2.8x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.8'.
1.428571429 + -10.14285714x + x2 = 0

Move the constant term to the right:

Add '-1.428571429' to each side of the equation.
1.428571429 + -10.14285714x + -1.428571429 + x2 = 0 + -1.428571429

Reorder the terms:
1.428571429 + -1.428571429 + -10.14285714x + x2 = 0 + -1.428571429

Combine like terms: 1.428571429 + -1.428571429 = 0.000000000
0.000000000 + -10.14285714x + x2 = 0 + -1.428571429
-10.14285714x + x2 = 0 + -1.428571429

Combine like terms: 0 + -1.428571429 = -1.428571429
-10.14285714x + x2 = -1.428571429

The x term is -10.14285714x.  Take half its coefficient (-5.07142857).
Square it (25.71938774) and add it to both sides.

Add '25.71938774' to each side of the equation.
-10.14285714x + 25.71938774 + x2 = -1.428571429 + 25.71938774

Reorder the terms:
25.71938774 + -10.14285714x + x2 = -1.428571429 + 25.71938774

Combine like terms: -1.428571429 + 25.71938774 = 24.290816311
25.71938774 + -10.14285714x + x2 = 24.290816311

Factor a perfect square on the left side:
(x + -5.07142857)(x + -5.07142857) = 24.290816311

Calculate the square root of the right side: 4.928571427

Break this problem into two subproblems by setting 
(x + -5.07142857) equal to 4.928571427 and -4.928571427.

Subproblem 1

x + -5.07142857 = 4.928571427 Simplifying x + -5.07142857 = 4.928571427 Reorder the terms: -5.07142857 + x = 4.928571427 Solving -5.07142857 + x = 4.928571427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.07142857' to each side of the equation. -5.07142857 + 5.07142857 + x = 4.928571427 + 5.07142857 Combine like terms: -5.07142857 + 5.07142857 = 0.00000000 0.00000000 + x = 4.928571427 + 5.07142857 x = 4.928571427 + 5.07142857 Combine like terms: 4.928571427 + 5.07142857 = 9.999999997 x = 9.999999997 Simplifying x = 9.999999997

Subproblem 2

x + -5.07142857 = -4.928571427 Simplifying x + -5.07142857 = -4.928571427 Reorder the terms: -5.07142857 + x = -4.928571427 Solving -5.07142857 + x = -4.928571427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.07142857' to each side of the equation. -5.07142857 + 5.07142857 + x = -4.928571427 + 5.07142857 Combine like terms: -5.07142857 + 5.07142857 = 0.00000000 0.00000000 + x = -4.928571427 + 5.07142857 x = -4.928571427 + 5.07142857 Combine like terms: -4.928571427 + 5.07142857 = 0.142857143 x = 0.142857143 Simplifying x = 0.142857143

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.999999997, 0.142857143}

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