x*x+49x-31=0

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Solution for x*x+49x-31=0 equation:


Simplifying
x * x + 49x + -31 = 0

Multiply x * x
x2 + 49x + -31 = 0

Reorder the terms:
-31 + 49x + x2 = 0

Solving
-31 + 49x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 49x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + 49x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 49x + x2 = 0 + 31
49x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
49x + x2 = 31

The x term is 49x.  Take half its coefficient (24.5).
Square it (600.25) and add it to both sides.

Add '600.25' to each side of the equation.
49x + 600.25 + x2 = 31 + 600.25

Reorder the terms:
600.25 + 49x + x2 = 31 + 600.25

Combine like terms: 31 + 600.25 = 631.25
600.25 + 49x + x2 = 631.25

Factor a perfect square on the left side:
(x + 24.5)(x + 24.5) = 631.25

Calculate the square root of the right side: 25.124689053

Break this problem into two subproblems by setting 
(x + 24.5) equal to 25.124689053 and -25.124689053.


Subproblem 1
x + 24.5 = 25.124689053

Simplifying
x + 24.5 = 25.124689053

Reorder the terms:
24.5 + x = 25.124689053

Solving
24.5 + x = 25.124689053

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-24.5' to each side of the equation.
24.5 + -24.5 + x = 25.124689053 + -24.5

Combine like terms: 24.5 + -24.5 = 0.0
0.0 + x = 25.124689053 + -24.5
x = 25.124689053 + -24.5

Combine like terms: 25.124689053 + -24.5 = 0.624689053
x = 0.624689053

Simplifying
x = 0.624689053


Subproblem 2
x + 24.5 = -25.124689053

Simplifying
x + 24.5 = -25.124689053

Reorder the terms:
24.5 + x = -25.124689053

Solving
24.5 + x = -25.124689053

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-24.5' to each side of the equation.
24.5 + -24.5 + x = -25.124689053 + -24.5

Combine like terms: 24.5 + -24.5 = 0.0
0.0 + x = -25.124689053 + -24.5
x = -25.124689053 + -24.5

Combine like terms: -25.124689053 + -24.5 = -49.624689053
x = -49.624689053

Simplifying
x = -49.624689053


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.624689053, -49.624689053}

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