x^2+4x-80=

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Solution for x^2+4x-80= equation:


Simplifying
x2 + 4x + -80 = 0

Reorder the terms:
-80 + 4x + x2 = 0

Solving
-80 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + 4x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + 4x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + 4x + x2 = 0 + 80
4x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
4x + x2 = 80

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 = 80 + 4

Reorder the terms:
4 + 4x + x2 = 80 + 4

Combine like terms: 80 + 4 = 84
4 + 4x + x2 = 84

Factor a perfect square on the left side:
(x + 2)(x + 2) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(x + 2) equal to 9.16515139 and -9.16515139.

Subproblem 1

x + 2 = 9.16515139 Simplifying x + 2 = 9.16515139 Reorder the terms: 2 + x = 9.16515139 Solving 2 + x = 9.16515139 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 = 9.16515139 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.16515139 + -2 x = 9.16515139 + -2 Combine like terms: 9.16515139 + -2 = 7.16515139 x = 7.16515139 Simplifying x = 7.16515139

Subproblem 2

x + 2 = -9.16515139 Simplifying x + 2 = -9.16515139 Reorder the terms: 2 + x = -9.16515139 Solving 2 + x = -9.16515139 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 = -9.16515139 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.16515139 + -2 x = -9.16515139 + -2 Combine like terms: -9.16515139 + -2 = -11.16515139 x = -11.16515139 Simplifying x = -11.16515139

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.16515139, -11.16515139}

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