(x-0.5)(3-7x)=0

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Solution for (x-0.5)(3-7x)=0 equation:


Simplifying
(x + -0.5)(3 + -7x) = 0

Reorder the terms:
(-0.5 + x)(3 + -7x) = 0

Multiply (-0.5 + x) * (3 + -7x)
(-0.5(3 + -7x) + x(3 + -7x)) = 0
((3 * -0.5 + -7x * -0.5) + x(3 + -7x)) = 0
((-1.5 + 3.5x) + x(3 + -7x)) = 0
(-1.5 + 3.5x + (3 * x + -7x * x)) = 0
(-1.5 + 3.5x + (3x + -7x2)) = 0

Combine like terms: 3.5x + 3x = 6.5x
(-1.5 + 6.5x + -7x2) = 0

Solving
-1.5 + 6.5x + -7x2 = 0

Solving for variable 'x'.

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

Divide each side by '-7'.
0.2142857143 + -0.9285714286x + x2 = 0

Move the constant term to the right:

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.9285714286x + -0.2142857143 + x2 = 0 + -0.2142857143

Reorder the terms:
0.2142857143 + -0.2142857143 + -0.9285714286x + x2 = 0 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + -0.9285714286x + x2 = 0 + -0.2142857143
-0.9285714286x + x2 = 0 + -0.2142857143

Combine like terms: 0 + -0.2142857143 = -0.2142857143
-0.9285714286x + x2 = -0.2142857143

The x term is -0.9285714286x.  Take half its coefficient (-0.4642857143).
Square it (0.2155612245) and add it to both sides.

Add '0.2155612245' to each side of the equation.
-0.9285714286x + 0.2155612245 + x2 = -0.2142857143 + 0.2155612245

Reorder the terms:
0.2155612245 + -0.9285714286x + x2 = -0.2142857143 + 0.2155612245

Combine like terms: -0.2142857143 + 0.2155612245 = 0.0012755102
0.2155612245 + -0.9285714286x + x2 = 0.0012755102

Factor a perfect square on the left side:
(x + -0.4642857143)(x + -0.4642857143) = 0.0012755102

Calculate the square root of the right side: 0.035714286

Break this problem into two subproblems by setting 
(x + -0.4642857143) equal to 0.035714286 and -0.035714286.

Subproblem 1

x + -0.4642857143 = 0.035714286 Simplifying x + -0.4642857143 = 0.035714286 Reorder the terms: -0.4642857143 + x = 0.035714286 Solving -0.4642857143 + x = 0.035714286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4642857143' to each side of the equation. -0.4642857143 + 0.4642857143 + x = 0.035714286 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + x = 0.035714286 + 0.4642857143 x = 0.035714286 + 0.4642857143 Combine like terms: 0.035714286 + 0.4642857143 = 0.5000000003 x = 0.5000000003 Simplifying x = 0.5000000003

Subproblem 2

x + -0.4642857143 = -0.035714286 Simplifying x + -0.4642857143 = -0.035714286 Reorder the terms: -0.4642857143 + x = -0.035714286 Solving -0.4642857143 + x = -0.035714286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4642857143' to each side of the equation. -0.4642857143 + 0.4642857143 + x = -0.035714286 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + x = -0.035714286 + 0.4642857143 x = -0.035714286 + 0.4642857143 Combine like terms: -0.035714286 + 0.4642857143 = 0.4285714283 x = 0.4285714283 Simplifying x = 0.4285714283

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.5000000003, 0.4285714283}

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