x*x=10x+14

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Solution for x*x=10x+14 equation:


Simplifying
x * x = 10x + 14

Multiply x * x
x2 = 10x + 14

Reorder the terms:
x2 = 14 + 10x

Solving
x2 = 14 + 10x

Solving for variable 'x'.

Reorder the terms:
-14 + -10x + x2 = 14 + 10x + -14 + -10x

Reorder the terms:
-14 + -10x + x2 = 14 + -14 + 10x + -10x

Combine like terms: 14 + -14 = 0
-14 + -10x + x2 = 0 + 10x + -10x
-14 + -10x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-14 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -10x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -10x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -10x + x2 = 0 + 14
-10x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-10x + x2 = 14

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 = 14 + 25

Reorder the terms:
25 + -10x + x2 = 14 + 25

Combine like terms: 14 + 25 = 39
25 + -10x + x2 = 39

Factor a perfect square on the left side:
(x + -5)(x + -5) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(x + -5) equal to 6.244997998 and -6.244997998.

Subproblem 1

x + -5 = 6.244997998 Simplifying x + -5 = 6.244997998 Reorder the terms: -5 + x = 6.244997998 Solving -5 + x = 6.244997998 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 = 6.244997998 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.244997998 + 5 x = 6.244997998 + 5 Combine like terms: 6.244997998 + 5 = 11.244997998 x = 11.244997998 Simplifying x = 11.244997998

Subproblem 2

x + -5 = -6.244997998 Simplifying x + -5 = -6.244997998 Reorder the terms: -5 + x = -6.244997998 Solving -5 + x = -6.244997998 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 = -6.244997998 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.244997998 + 5 x = -6.244997998 + 5 Combine like terms: -6.244997998 + 5 = -1.244997998 x = -1.244997998 Simplifying x = -1.244997998

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.244997998, -1.244997998}

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