2x+7(10x+200)=x(x+5)

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Solution for 2x+7(10x+200)=x(x+5) equation:


Simplifying
2x + 7(10x + 200) = x(x + 5)

Reorder the terms:
2x + 7(200 + 10x) = x(x + 5)
2x + (200 * 7 + 10x * 7) = x(x + 5)
2x + (1400 + 70x) = x(x + 5)

Reorder the terms:
1400 + 2x + 70x = x(x + 5)

Combine like terms: 2x + 70x = 72x
1400 + 72x = x(x + 5)

Reorder the terms:
1400 + 72x = x(5 + x)
1400 + 72x = (5 * x + x * x)
1400 + 72x = (5x + x2)

Solving
1400 + 72x = 5x + x2

Solving for variable 'x'.

Combine like terms: 72x + -5x = 67x
1400 + 67x + -1x2 = 5x + x2 + -5x + -1x2

Reorder the terms:
1400 + 67x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
1400 + 67x + -1x2 = 0 + x2 + -1x2
1400 + 67x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1400 + 67x + -1x2 = 0

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

Divide each side by '-1'.
-1400 + -67x + x2 = 0

Move the constant term to the right:

Add '1400' to each side of the equation.
-1400 + -67x + 1400 + x2 = 0 + 1400

Reorder the terms:
-1400 + 1400 + -67x + x2 = 0 + 1400

Combine like terms: -1400 + 1400 = 0
0 + -67x + x2 = 0 + 1400
-67x + x2 = 0 + 1400

Combine like terms: 0 + 1400 = 1400
-67x + x2 = 1400

The x term is -67x.  Take half its coefficient (-33.5).
Square it (1122.25) and add it to both sides.

Add '1122.25' to each side of the equation.
-67x + 1122.25 + x2 = 1400 + 1122.25

Reorder the terms:
1122.25 + -67x + x2 = 1400 + 1122.25

Combine like terms: 1400 + 1122.25 = 2522.25
1122.25 + -67x + x2 = 2522.25

Factor a perfect square on the left side:
(x + -33.5)(x + -33.5) = 2522.25

Calculate the square root of the right side: 50.222007128

Break this problem into two subproblems by setting 
(x + -33.5) equal to 50.222007128 and -50.222007128.

Subproblem 1

x + -33.5 = 50.222007128 Simplifying x + -33.5 = 50.222007128 Reorder the terms: -33.5 + x = 50.222007128 Solving -33.5 + x = 50.222007128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33.5' to each side of the equation. -33.5 + 33.5 + x = 50.222007128 + 33.5 Combine like terms: -33.5 + 33.5 = 0.0 0.0 + x = 50.222007128 + 33.5 x = 50.222007128 + 33.5 Combine like terms: 50.222007128 + 33.5 = 83.722007128 x = 83.722007128 Simplifying x = 83.722007128

Subproblem 2

x + -33.5 = -50.222007128 Simplifying x + -33.5 = -50.222007128 Reorder the terms: -33.5 + x = -50.222007128 Solving -33.5 + x = -50.222007128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33.5' to each side of the equation. -33.5 + 33.5 + x = -50.222007128 + 33.5 Combine like terms: -33.5 + 33.5 = 0.0 0.0 + x = -50.222007128 + 33.5 x = -50.222007128 + 33.5 Combine like terms: -50.222007128 + 33.5 = -16.722007128 x = -16.722007128 Simplifying x = -16.722007128

Solution

The solution to the problem is based on the solutions from the subproblems. x = {83.722007128, -16.722007128}

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