x(x-10)=(x-5)(2x+7)

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Solution for x(x-10)=(x-5)(2x+7) equation:


Simplifying
x(x + -10) = (x + -5)(2x + 7)

Reorder the terms:
x(-10 + x) = (x + -5)(2x + 7)
(-10 * x + x * x) = (x + -5)(2x + 7)
(-10x + x2) = (x + -5)(2x + 7)

Reorder the terms:
-10x + x2 = (-5 + x)(2x + 7)

Reorder the terms:
-10x + x2 = (-5 + x)(7 + 2x)

Multiply (-5 + x) * (7 + 2x)
-10x + x2 = (-5(7 + 2x) + x(7 + 2x))
-10x + x2 = ((7 * -5 + 2x * -5) + x(7 + 2x))
-10x + x2 = ((-35 + -10x) + x(7 + 2x))
-10x + x2 = (-35 + -10x + (7 * x + 2x * x))
-10x + x2 = (-35 + -10x + (7x + 2x2))

Combine like terms: -10x + 7x = -3x
-10x + x2 = (-35 + -3x + 2x2)

Solving
-10x + x2 = -35 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
35 + -10x + 3x + x2 + -2x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2

Combine like terms: -10x + 3x = -7x
35 + -7x + x2 + -2x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2

Combine like terms: x2 + -2x2 = -1x2
35 + -7x + -1x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2

Reorder the terms:
35 + -7x + -1x2 = -35 + 35 + -3x + 3x + 2x2 + -2x2

Combine like terms: -35 + 35 = 0
35 + -7x + -1x2 = 0 + -3x + 3x + 2x2 + -2x2
35 + -7x + -1x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
35 + -7x + -1x2 = 0 + 2x2 + -2x2
35 + -7x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
35 + -7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-35 + 7x + x2 = 0

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 7x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + 7x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 7x + x2 = 0 + 35
7x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
7x + x2 = 35

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 35 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 35 + 12.25

Combine like terms: 35 + 12.25 = 47.25
12.25 + 7x + x2 = 47.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 47.25

Calculate the square root of the right side: 6.873863542

Break this problem into two subproblems by setting 
(x + 3.5) equal to 6.873863542 and -6.873863542.

Subproblem 1

x + 3.5 = 6.873863542 Simplifying x + 3.5 = 6.873863542 Reorder the terms: 3.5 + x = 6.873863542 Solving 3.5 + x = 6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 6.873863542 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.873863542 + -3.5 x = 6.873863542 + -3.5 Combine like terms: 6.873863542 + -3.5 = 3.373863542 x = 3.373863542 Simplifying x = 3.373863542

Subproblem 2

x + 3.5 = -6.873863542 Simplifying x + 3.5 = -6.873863542 Reorder the terms: 3.5 + x = -6.873863542 Solving 3.5 + x = -6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -6.873863542 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.873863542 + -3.5 x = -6.873863542 + -3.5 Combine like terms: -6.873863542 + -3.5 = -10.373863542 x = -10.373863542 Simplifying x = -10.373863542

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.373863542, -10.373863542}

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