x^2+x+10=10x

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Solution for x^2+x+10=10x equation:


Simplifying
x2 + x + 10 = 10x

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

Solving
10 + x + x2 = 10x

Solving for variable 'x'.

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

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

Combine like terms: 10x + -10x = 0
10 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -9x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -9x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -9x + x2 = 0 + -10
-9x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-9x + x2 = -10

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 = -10 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -10 + 20.25

Combine like terms: -10 + 20.25 = 10.25
20.25 + -9x + x2 = 10.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

x + -4.5 = 3.201562119 Simplifying x + -4.5 = 3.201562119 Reorder the terms: -4.5 + x = 3.201562119 Solving -4.5 + x = 3.201562119 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 = 3.201562119 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.201562119 + 4.5 x = 3.201562119 + 4.5 Combine like terms: 3.201562119 + 4.5 = 7.701562119 x = 7.701562119 Simplifying x = 7.701562119

Subproblem 2

x + -4.5 = -3.201562119 Simplifying x + -4.5 = -3.201562119 Reorder the terms: -4.5 + x = -3.201562119 Solving -4.5 + x = -3.201562119 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 = -3.201562119 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.201562119 + 4.5 x = -3.201562119 + 4.5 Combine like terms: -3.201562119 + 4.5 = 1.298437881 x = 1.298437881 Simplifying x = 1.298437881

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.701562119, 1.298437881}

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