x(x+10)=x+7

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Solution for x(x+10)=x+7 equation:


Simplifying
x(x + 10) = x + 7

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

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

Solving
10x + x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
-7 + 10x + -1x + x2 = 7 + x + -7 + -1x

Combine like terms: 10x + -1x = 9x
-7 + 9x + x2 = 7 + x + -7 + -1x

Reorder the terms:
-7 + 9x + x2 = 7 + -7 + x + -1x

Combine like terms: 7 + -7 = 0
-7 + 9x + x2 = 0 + x + -1x
-7 + 9x + x2 = x + -1x

Combine like terms: x + -1x = 0
-7 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 9x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 9x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 9x + x2 = 0 + 7
9x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
9x + x2 = 7

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 7 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 7 + 20.25

Combine like terms: 7 + 20.25 = 27.25
20.25 + 9x + x2 = 27.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5.220153254 and -5.220153254.

Subproblem 1

x + 4.5 = 5.220153254 Simplifying x + 4.5 = 5.220153254 Reorder the terms: 4.5 + x = 5.220153254 Solving 4.5 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.220153254 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.220153254 + -4.5 x = 5.220153254 + -4.5 Combine like terms: 5.220153254 + -4.5 = 0.720153254 x = 0.720153254 Simplifying x = 0.720153254

Subproblem 2

x + 4.5 = -5.220153254 Simplifying x + 4.5 = -5.220153254 Reorder the terms: 4.5 + x = -5.220153254 Solving 4.5 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.220153254 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.220153254 + -4.5 x = -5.220153254 + -4.5 Combine like terms: -5.220153254 + -4.5 = -9.720153254 x = -9.720153254 Simplifying x = -9.720153254

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.720153254, -9.720153254}

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