x(2x-7)=10

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


Simplifying
x(2x + -7) = 10

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

Solving
-7x + 2x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -7x + 2x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -7x + 2x2 = 0

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

Divide each side by '2'.
-5 + -3.5x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -3.5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -3.5x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3.5x + x2 = 0 + 5
-3.5x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-3.5x + x2 = 5

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 5 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 5 + 3.0625

Combine like terms: 5 + 3.0625 = 8.0625
3.0625 + -3.5x + x2 = 8.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.839454173 and -2.839454173.


Subproblem 1
x + -1.75 = 2.839454173

Simplifying
x + -1.75 = 2.839454173

Reorder the terms:
-1.75 + x = 2.839454173

Solving
-1.75 + x = 2.839454173

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 2.839454173 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 2.839454173 + 1.75
x = 2.839454173 + 1.75

Combine like terms: 2.839454173 + 1.75 = 4.589454173
x = 4.589454173

Simplifying
x = 4.589454173


Subproblem 2
x + -1.75 = -2.839454173

Simplifying
x + -1.75 = -2.839454173

Reorder the terms:
-1.75 + x = -2.839454173

Solving
-1.75 + x = -2.839454173

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -2.839454173 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -2.839454173 + 1.75
x = -2.839454173 + 1.75

Combine like terms: -2.839454173 + 1.75 = -1.089454173
x = -1.089454173

Simplifying
x = -1.089454173


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.589454173, -1.089454173}

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