7x(x-10)=2x-7

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Solution for 7x(x-10)=2x-7 equation:


Simplifying
7x(x + -10) = 2x + -7

Reorder the terms:
7x(-10 + x) = 2x + -7
(-10 * 7x + x * 7x) = 2x + -7
(-70x + 7x2) = 2x + -7

Reorder the terms:
-70x + 7x2 = -7 + 2x

Solving
-70x + 7x2 = -7 + 2x

Solving for variable 'x'.

Reorder the terms:
7 + -70x + -2x + 7x2 = -7 + 2x + 7 + -2x

Combine like terms: -70x + -2x = -72x
7 + -72x + 7x2 = -7 + 2x + 7 + -2x

Reorder the terms:
7 + -72x + 7x2 = -7 + 7 + 2x + -2x

Combine like terms: -7 + 7 = 0
7 + -72x + 7x2 = 0 + 2x + -2x
7 + -72x + 7x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
7 + -72x + 7x2 = 0

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

Divide each side by '7'.
1 + -10.28571429x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -10.28571429x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -10.28571429x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10.28571429x + x2 = 0 + -1
-10.28571429x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-10.28571429x + x2 = -1

The x term is -10.28571429x.  Take half its coefficient (-5.142857145).
Square it (26.44897961) and add it to both sides.

Add '26.44897961' to each side of the equation.
-10.28571429x + 26.44897961 + x2 = -1 + 26.44897961

Reorder the terms:
26.44897961 + -10.28571429x + x2 = -1 + 26.44897961

Combine like terms: -1 + 26.44897961 = 25.44897961
26.44897961 + -10.28571429x + x2 = 25.44897961

Factor a perfect square on the left side:
(x + -5.142857145)(x + -5.142857145) = 25.44897961

Calculate the square root of the right side: 5.044698168

Break this problem into two subproblems by setting 
(x + -5.142857145) equal to 5.044698168 and -5.044698168.

Subproblem 1

x + -5.142857145 = 5.044698168 Simplifying x + -5.142857145 = 5.044698168 Reorder the terms: -5.142857145 + x = 5.044698168 Solving -5.142857145 + x = 5.044698168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.142857145' to each side of the equation. -5.142857145 + 5.142857145 + x = 5.044698168 + 5.142857145 Combine like terms: -5.142857145 + 5.142857145 = 0.000000000 0.000000000 + x = 5.044698168 + 5.142857145 x = 5.044698168 + 5.142857145 Combine like terms: 5.044698168 + 5.142857145 = 10.187555313 x = 10.187555313 Simplifying x = 10.187555313

Subproblem 2

x + -5.142857145 = -5.044698168 Simplifying x + -5.142857145 = -5.044698168 Reorder the terms: -5.142857145 + x = -5.044698168 Solving -5.142857145 + x = -5.044698168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.142857145' to each side of the equation. -5.142857145 + 5.142857145 + x = -5.044698168 + 5.142857145 Combine like terms: -5.142857145 + 5.142857145 = 0.000000000 0.000000000 + x = -5.044698168 + 5.142857145 x = -5.044698168 + 5.142857145 Combine like terms: -5.044698168 + 5.142857145 = 0.098158977 x = 0.098158977 Simplifying x = 0.098158977

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.187555313, 0.098158977}

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