x^2+80x+5=49

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Solution for x^2+80x+5=49 equation:


Simplifying
x2 + 80x + 5 = 49

Reorder the terms:
5 + 80x + x2 = 49

Solving
5 + 80x + x2 = 49

Solving for variable 'x'.

Reorder the terms:
5 + -49 + 80x + x2 = 49 + -49

Combine like terms: 5 + -49 = -44
-44 + 80x + x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-44 + 80x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + 80x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + 80x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + 80x + x2 = 0 + 44
80x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
80x + x2 = 44

The x term is 80x.  Take half its coefficient (40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
80x + 1600 + x2 = 44 + 1600

Reorder the terms:
1600 + 80x + x2 = 44 + 1600

Combine like terms: 44 + 1600 = 1644
1600 + 80x + x2 = 1644

Factor a perfect square on the left side:
(x + 40)(x + 40) = 1644

Calculate the square root of the right side: 40.546269865

Break this problem into two subproblems by setting 
(x + 40) equal to 40.546269865 and -40.546269865.

Subproblem 1

x + 40 = 40.546269865 Simplifying x + 40 = 40.546269865 Reorder the terms: 40 + x = 40.546269865 Solving 40 + x = 40.546269865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 40.546269865 + -40 Combine like terms: 40 + -40 = 0 0 + x = 40.546269865 + -40 x = 40.546269865 + -40 Combine like terms: 40.546269865 + -40 = 0.546269865 x = 0.546269865 Simplifying x = 0.546269865

Subproblem 2

x + 40 = -40.546269865 Simplifying x + 40 = -40.546269865 Reorder the terms: 40 + x = -40.546269865 Solving 40 + x = -40.546269865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -40.546269865 + -40 Combine like terms: 40 + -40 = 0 0 + x = -40.546269865 + -40 x = -40.546269865 + -40 Combine like terms: -40.546269865 + -40 = -80.546269865 x = -80.546269865 Simplifying x = -80.546269865

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.546269865, -80.546269865}

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