x^2-19x+33=0

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Solution for x^2-19x+33=0 equation:


Simplifying
x2 + -19x + 33 = 0

Reorder the terms:
33 + -19x + x2 = 0

Solving
33 + -19x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-33' to each side of the equation.
33 + -19x + -33 + x2 = 0 + -33

Reorder the terms:
33 + -33 + -19x + x2 = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -19x + x2 = 0 + -33
-19x + x2 = 0 + -33

Combine like terms: 0 + -33 = -33
-19x + x2 = -33

The x term is -19x.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19x + 90.25 + x2 = -33 + 90.25

Reorder the terms:
90.25 + -19x + x2 = -33 + 90.25

Combine like terms: -33 + 90.25 = 57.25
90.25 + -19x + x2 = 57.25

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 57.25

Calculate the square root of the right side: 7.566372975

Break this problem into two subproblems by setting 
(x + -9.5) equal to 7.566372975 and -7.566372975.

Subproblem 1

x + -9.5 = 7.566372975 Simplifying x + -9.5 = 7.566372975 Reorder the terms: -9.5 + x = 7.566372975 Solving -9.5 + x = 7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 7.566372975 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 7.566372975 + 9.5 x = 7.566372975 + 9.5 Combine like terms: 7.566372975 + 9.5 = 17.066372975 x = 17.066372975 Simplifying x = 17.066372975

Subproblem 2

x + -9.5 = -7.566372975 Simplifying x + -9.5 = -7.566372975 Reorder the terms: -9.5 + x = -7.566372975 Solving -9.5 + x = -7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -7.566372975 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -7.566372975 + 9.5 x = -7.566372975 + 9.5 Combine like terms: -7.566372975 + 9.5 = 1.933627025 x = 1.933627025 Simplifying x = 1.933627025

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.066372975, 1.933627025}

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