7x(x-2)=5

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Solution for 7x(x-2)=5 equation:


Simplifying
7x(x + -2) = 5

Reorder the terms:
7x(-2 + x) = 5
(-2 * 7x + x * 7x) = 5
(-14x + 7x2) = 5

Solving
-14x + 7x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -14x + 7x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -14x + 7x2 = 0

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

Divide each side by '7'.
-0.7142857143 + -2x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + -2x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + -2x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + 0.7142857143
-2x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
-2x + x2 = 0.7142857143

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 0.7142857143 + 1

Reorder the terms:
1 + -2x + x2 = 0.7142857143 + 1

Combine like terms: 0.7142857143 + 1 = 1.7142857143
1 + -2x + x2 = 1.7142857143

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.7142857143

Calculate the square root of the right side: 1.309307341

Break this problem into two subproblems by setting 
(x + -1) equal to 1.309307341 and -1.309307341.

Subproblem 1

x + -1 = 1.309307341 Simplifying x + -1 = 1.309307341 Reorder the terms: -1 + x = 1.309307341 Solving -1 + x = 1.309307341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.309307341 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.309307341 + 1 x = 1.309307341 + 1 Combine like terms: 1.309307341 + 1 = 2.309307341 x = 2.309307341 Simplifying x = 2.309307341

Subproblem 2

x + -1 = -1.309307341 Simplifying x + -1 = -1.309307341 Reorder the terms: -1 + x = -1.309307341 Solving -1 + x = -1.309307341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.309307341 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.309307341 + 1 x = -1.309307341 + 1 Combine like terms: -1.309307341 + 1 = -0.309307341 x = -0.309307341 Simplifying x = -0.309307341

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.309307341, -0.309307341}

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