x(x-5)=x(2)+4x+7

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Solution for x(x-5)=x(2)+4x+7 equation:


Simplifying
x(x + -5) = x(2) + 4x + 7

Reorder the terms:
x(-5 + x) = x(2) + 4x + 7
(-5 * x + x * x) = x(2) + 4x + 7
(-5x + x2) = x(2) + 4x + 7

Reorder the terms for easier multiplication:
-5x + x2 = 2x + 4x + 7

Reorder the terms:
-5x + x2 = 7 + 2x + 4x

Combine like terms: 2x + 4x = 6x
-5x + x2 = 7 + 6x

Solving
-5x + x2 = 7 + 6x

Solving for variable 'x'.

Reorder the terms:
-7 + -5x + -6x + x2 = 7 + 6x + -7 + -6x

Combine like terms: -5x + -6x = -11x
-7 + -11x + x2 = 7 + 6x + -7 + -6x

Reorder the terms:
-7 + -11x + x2 = 7 + -7 + 6x + -6x

Combine like terms: 7 + -7 = 0
-7 + -11x + x2 = 0 + 6x + -6x
-7 + -11x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-7 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -11x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -11x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -11x + x2 = 0 + 7
-11x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-11x + x2 = 7

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = 7 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 7 + 30.25

Combine like terms: 7 + 30.25 = 37.25
30.25 + -11x + x2 = 37.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(x + -5.5) equal to 6.103277808 and -6.103277808.

Subproblem 1

x + -5.5 = 6.103277808 Simplifying x + -5.5 = 6.103277808 Reorder the terms: -5.5 + x = 6.103277808 Solving -5.5 + x = 6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 6.103277808 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.103277808 + 5.5 x = 6.103277808 + 5.5 Combine like terms: 6.103277808 + 5.5 = 11.603277808 x = 11.603277808 Simplifying x = 11.603277808

Subproblem 2

x + -5.5 = -6.103277808 Simplifying x + -5.5 = -6.103277808 Reorder the terms: -5.5 + x = -6.103277808 Solving -5.5 + x = -6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -6.103277808 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.103277808 + 5.5 x = -6.103277808 + 5.5 Combine like terms: -6.103277808 + 5.5 = -0.603277808 x = -0.603277808 Simplifying x = -0.603277808

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.603277808, -0.603277808}

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