4x=x^2-110

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Solution for 4x=x^2-110 equation:


Simplifying
4x = x2 + -110

Reorder the terms:
4x = -110 + x2

Solving
4x = -110 + x2

Solving for variable 'x'.

Reorder the terms:
110 + 4x + -1x2 = -110 + x2 + 110 + -1x2

Reorder the terms:
110 + 4x + -1x2 = -110 + 110 + x2 + -1x2

Combine like terms: -110 + 110 = 0
110 + 4x + -1x2 = 0 + x2 + -1x2
110 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
110 + 4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-110 + -4x + x2 = 0

Move the constant term to the right:

Add '110' to each side of the equation.
-110 + -4x + 110 + x2 = 0 + 110

Reorder the terms:
-110 + 110 + -4x + x2 = 0 + 110

Combine like terms: -110 + 110 = 0
0 + -4x + x2 = 0 + 110
-4x + x2 = 0 + 110

Combine like terms: 0 + 110 = 110
-4x + x2 = 110

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 110 + 4

Reorder the terms:
4 + -4x + x2 = 110 + 4

Combine like terms: 110 + 4 = 114
4 + -4x + x2 = 114

Factor a perfect square on the left side:
(x + -2)(x + -2) = 114

Calculate the square root of the right side: 10.677078252

Break this problem into two subproblems by setting 
(x + -2) equal to 10.677078252 and -10.677078252.

Subproblem 1

x + -2 = 10.677078252 Simplifying x + -2 = 10.677078252 Reorder the terms: -2 + x = 10.677078252 Solving -2 + x = 10.677078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 10.677078252 + 2 Combine like terms: -2 + 2 = 0 0 + x = 10.677078252 + 2 x = 10.677078252 + 2 Combine like terms: 10.677078252 + 2 = 12.677078252 x = 12.677078252 Simplifying x = 12.677078252

Subproblem 2

x + -2 = -10.677078252 Simplifying x + -2 = -10.677078252 Reorder the terms: -2 + x = -10.677078252 Solving -2 + x = -10.677078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -10.677078252 + 2 Combine like terms: -2 + 2 = 0 0 + x = -10.677078252 + 2 x = -10.677078252 + 2 Combine like terms: -10.677078252 + 2 = -8.677078252 x = -8.677078252 Simplifying x = -8.677078252

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.677078252, -8.677078252}

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