x^2-20x+35=0

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Solution for x^2-20x+35=0 equation:


Simplifying
x2 + -20x + 35 = 0

Reorder the terms:
35 + -20x + x2 = 0

Solving
35 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -20x + -35 + x2 = 0 + -35

Reorder the terms:
35 + -35 + -20x + x2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -20x + x2 = 0 + -35
-20x + x2 = 0 + -35

Combine like terms: 0 + -35 = -35
-20x + x2 = -35

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -35 + 100

Reorder the terms:
100 + -20x + x2 = -35 + 100

Combine like terms: -35 + 100 = 65
100 + -20x + x2 = 65

Factor a perfect square on the left side:
(x + -10)(x + -10) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(x + -10) equal to 8.062257748 and -8.062257748.

Subproblem 1

x + -10 = 8.062257748 Simplifying x + -10 = 8.062257748 Reorder the terms: -10 + x = 8.062257748 Solving -10 + x = 8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 8.062257748 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.062257748 + 10 x = 8.062257748 + 10 Combine like terms: 8.062257748 + 10 = 18.062257748 x = 18.062257748 Simplifying x = 18.062257748

Subproblem 2

x + -10 = -8.062257748 Simplifying x + -10 = -8.062257748 Reorder the terms: -10 + x = -8.062257748 Solving -10 + x = -8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -8.062257748 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.062257748 + 10 x = -8.062257748 + 10 Combine like terms: -8.062257748 + 10 = 1.937742252 x = 1.937742252 Simplifying x = 1.937742252

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.062257748, 1.937742252}

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