x^2-7+10x=0

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Solution for x^2-7+10x=0 equation: 


Simplifying
x2 + -7 + 10x = 0

Reorder the terms:
-7 + 10x + x2 = 0

Solving
-7 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 10x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 10x + x2 = 0 + 7

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

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

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 7 + 25

Reorder the terms:
25 + 10x + x2 = 7 + 25

Combine like terms: 7 + 25 = 32
25 + 10x + x2 = 32

Factor a perfect square on the left side:
(x + 5)(x + 5) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + 5) equal to 5.656854249 and -5.656854249.


Subproblem 1
x + 5 = 5.656854249

Simplifying
x + 5 = 5.656854249

Reorder the terms:
5 + x = 5.656854249

Solving
5 + x = 5.656854249

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 5.656854249 + -5

Combine like terms: 5 + -5 = 0
0 + x = 5.656854249 + -5
x = 5.656854249 + -5

Combine like terms: 5.656854249 + -5 = 0.656854249
x = 0.656854249

Simplifying
x = 0.656854249


Subproblem 2
x + 5 = -5.656854249

Simplifying
x + 5 = -5.656854249

Reorder the terms:
5 + x = -5.656854249

Solving
5 + x = -5.656854249

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -5.656854249 + -5

Combine like terms: 5 + -5 = 0
0 + x = -5.656854249 + -5
x = -5.656854249 + -5

Combine like terms: -5.656854249 + -5 = -10.656854249
x = -10.656854249

Simplifying
x = -10.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.656854249, -10.656854249}

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