x^2-21x+25=0

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Solution for x^2-21x+25=0 equation:


Simplifying
x2 + -21x + 25 = 0

Reorder the terms:
25 + -21x + x2 = 0

Solving
25 + -21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -21x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + -21x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -21x + x2 = 0 + -25
-21x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
-21x + x2 = -25

The x term is -21x.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21x + 110.25 + x2 = -25 + 110.25

Reorder the terms:
110.25 + -21x + x2 = -25 + 110.25

Combine like terms: -25 + 110.25 = 85.25
110.25 + -21x + x2 = 85.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 85.25

Calculate the square root of the right side: 9.233092656

Break this problem into two subproblems by setting 
(x + -10.5) equal to 9.233092656 and -9.233092656.

Subproblem 1

x + -10.5 = 9.233092656 Simplifying x + -10.5 = 9.233092656 Reorder the terms: -10.5 + x = 9.233092656 Solving -10.5 + x = 9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 9.233092656 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 9.233092656 + 10.5 x = 9.233092656 + 10.5 Combine like terms: 9.233092656 + 10.5 = 19.733092656 x = 19.733092656 Simplifying x = 19.733092656

Subproblem 2

x + -10.5 = -9.233092656 Simplifying x + -10.5 = -9.233092656 Reorder the terms: -10.5 + x = -9.233092656 Solving -10.5 + x = -9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -9.233092656 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -9.233092656 + 10.5 x = -9.233092656 + 10.5 Combine like terms: -9.233092656 + 10.5 = 1.266907344 x = 1.266907344 Simplifying x = 1.266907344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.733092656, 1.266907344}

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