x^2-100x+1700=0

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Solution for x^2-100x+1700=0 equation:


Simplifying
x2 + -100x + 1700 = 0

Reorder the terms:
1700 + -100x + x2 = 0

Solving
1700 + -100x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1700' to each side of the equation.
1700 + -100x + -1700 + x2 = 0 + -1700

Reorder the terms:
1700 + -1700 + -100x + x2 = 0 + -1700

Combine like terms: 1700 + -1700 = 0
0 + -100x + x2 = 0 + -1700
-100x + x2 = 0 + -1700

Combine like terms: 0 + -1700 = -1700
-100x + x2 = -1700

The x term is -100x.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x + 2500 + x2 = -1700 + 2500

Reorder the terms:
2500 + -100x + x2 = -1700 + 2500

Combine like terms: -1700 + 2500 = 800
2500 + -100x + x2 = 800

Factor a perfect square on the left side:
(x + -50)(x + -50) = 800

Calculate the square root of the right side: 28.284271247

Break this problem into two subproblems by setting 
(x + -50) equal to 28.284271247 and -28.284271247.

Subproblem 1

x + -50 = 28.284271247 Simplifying x + -50 = 28.284271247 Reorder the terms: -50 + x = 28.284271247 Solving -50 + x = 28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 28.284271247 + 50 Combine like terms: -50 + 50 = 0 0 + x = 28.284271247 + 50 x = 28.284271247 + 50 Combine like terms: 28.284271247 + 50 = 78.284271247 x = 78.284271247 Simplifying x = 78.284271247

Subproblem 2

x + -50 = -28.284271247 Simplifying x + -50 = -28.284271247 Reorder the terms: -50 + x = -28.284271247 Solving -50 + x = -28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -28.284271247 + 50 Combine like terms: -50 + 50 = 0 0 + x = -28.284271247 + 50 x = -28.284271247 + 50 Combine like terms: -28.284271247 + 50 = 21.715728753 x = 21.715728753 Simplifying x = 21.715728753

Solution

The solution to the problem is based on the solutions from the subproblems. x = {78.284271247, 21.715728753}

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