4x+x^2-160=0

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Solution for 4x+x^2-160=0 equation:


Simplifying
4x + x2 + -160 = 0

Reorder the terms:
-160 + 4x + x2 = 0

Solving
-160 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '160' to each side of the equation.
-160 + 4x + 160 + x2 = 0 + 160

Reorder the terms:
-160 + 160 + 4x + x2 = 0 + 160

Combine like terms: -160 + 160 = 0
0 + 4x + x2 = 0 + 160
4x + x2 = 0 + 160

Combine like terms: 0 + 160 = 160
4x + x2 = 160

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 = 160 + 4

Reorder the terms:
4 + 4x + x2 = 160 + 4

Combine like terms: 160 + 4 = 164
4 + 4x + x2 = 164

Factor a perfect square on the left side:
(x + 2)(x + 2) = 164

Calculate the square root of the right side: 12.806248475

Break this problem into two subproblems by setting 
(x + 2) equal to 12.806248475 and -12.806248475.

Subproblem 1

x + 2 = 12.806248475 Simplifying x + 2 = 12.806248475 Reorder the terms: 2 + x = 12.806248475 Solving 2 + x = 12.806248475 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 = 12.806248475 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.806248475 + -2 x = 12.806248475 + -2 Combine like terms: 12.806248475 + -2 = 10.806248475 x = 10.806248475 Simplifying x = 10.806248475

Subproblem 2

x + 2 = -12.806248475 Simplifying x + 2 = -12.806248475 Reorder the terms: 2 + x = -12.806248475 Solving 2 + x = -12.806248475 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 = -12.806248475 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.806248475 + -2 x = -12.806248475 + -2 Combine like terms: -12.806248475 + -2 = -14.806248475 x = -14.806248475 Simplifying x = -14.806248475

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.806248475, -14.806248475}

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