x^2-49x+70=0

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Solution for x^2-49x+70=0 equation: 


Simplifying
x2 + -49x + 70 = 0

Reorder the terms:
70 + -49x + x2 = 0

Solving
70 + -49x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-70' to each side of the equation.
70 + -49x + -70 + x2 = 0 + -70

Reorder the terms:
70 + -70 + -49x + x2 = 0 + -70

Combine like terms: 70 + -70 = 0
0 + -49x + x2 = 0 + -70
-49x + x2 = 0 + -70

Combine like terms: 0 + -70 = -70
-49x + x2 = -70

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 = -70 + 600.25

Reorder the terms:
600.25 + -49x + x2 = -70 + 600.25

Combine like terms: -70 + 600.25 = 530.25
600.25 + -49x + x2 = 530.25

Factor a perfect square on the left side:
(x + -24.5)(x + -24.5) = 530.25

Calculate the square root of the right side: 23.027157879

Break this problem into two subproblems by setting 
(x + -24.5) equal to 23.027157879 and -23.027157879.


Subproblem 1
x + -24.5 = 23.027157879

Simplifying
x + -24.5 = 23.027157879

Reorder the terms:
-24.5 + x = 23.027157879

Solving
-24.5 + x = 23.027157879

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 = 23.027157879 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + x = 23.027157879 + 24.5
x = 23.027157879 + 24.5

Combine like terms: 23.027157879 + 24.5 = 47.527157879
x = 47.527157879

Simplifying
x = 47.527157879


Subproblem 2
x + -24.5 = -23.027157879

Simplifying
x + -24.5 = -23.027157879

Reorder the terms:
-24.5 + x = -23.027157879

Solving
-24.5 + x = -23.027157879

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 = -23.027157879 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + x = -23.027157879 + 24.5
x = -23.027157879 + 24.5

Combine like terms: -23.027157879 + 24.5 = 1.472842121
x = 1.472842121

Simplifying
x = 1.472842121


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {47.527157879, 1.472842121}

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