x^2-42x+56=0

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Solution for x^2-42x+56=0 equation:


Simplifying
x2 + -42x + 56 = 0

Reorder the terms:
56 + -42x + x2 = 0

Solving
56 + -42x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-56' to each side of the equation.
56 + -42x + -56 + x2 = 0 + -56

Reorder the terms:
56 + -56 + -42x + x2 = 0 + -56

Combine like terms: 56 + -56 = 0
0 + -42x + x2 = 0 + -56
-42x + x2 = 0 + -56

Combine like terms: 0 + -56 = -56
-42x + x2 = -56

The x term is -42x.  Take half its coefficient (-21).
Square it (441) and add it to both sides.

Add '441' to each side of the equation.
-42x + 441 + x2 = -56 + 441

Reorder the terms:
441 + -42x + x2 = -56 + 441

Combine like terms: -56 + 441 = 385
441 + -42x + x2 = 385

Factor a perfect square on the left side:
(x + -21)(x + -21) = 385

Calculate the square root of the right side: 19.62141687

Break this problem into two subproblems by setting 
(x + -21) equal to 19.62141687 and -19.62141687.

Subproblem 1

x + -21 = 19.62141687 Simplifying x + -21 = 19.62141687 Reorder the terms: -21 + x = 19.62141687 Solving -21 + x = 19.62141687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 19.62141687 + 21 Combine like terms: -21 + 21 = 0 0 + x = 19.62141687 + 21 x = 19.62141687 + 21 Combine like terms: 19.62141687 + 21 = 40.62141687 x = 40.62141687 Simplifying x = 40.62141687

Subproblem 2

x + -21 = -19.62141687 Simplifying x + -21 = -19.62141687 Reorder the terms: -21 + x = -19.62141687 Solving -21 + x = -19.62141687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -19.62141687 + 21 Combine like terms: -21 + 21 = 0 0 + x = -19.62141687 + 21 x = -19.62141687 + 21 Combine like terms: -19.62141687 + 21 = 1.37858313 x = 1.37858313 Simplifying x = 1.37858313

Solution

The solution to the problem is based on the solutions from the subproblems. x = {40.62141687, 1.37858313}

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