x^2-100x+1400=0

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Solution for x^2-100x+1400=0 equation:


Simplifying
x2 + -100x + 1400 = 0

Reorder the terms:
1400 + -100x + x2 = 0

Solving
1400 + -100x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1400' to each side of the equation.
1400 + -100x + -1400 + x2 = 0 + -1400

Reorder the terms:
1400 + -1400 + -100x + x2 = 0 + -1400

Combine like terms: 1400 + -1400 = 0
0 + -100x + x2 = 0 + -1400
-100x + x2 = 0 + -1400

Combine like terms: 0 + -1400 = -1400
-100x + x2 = -1400

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 = -1400 + 2500

Reorder the terms:
2500 + -100x + x2 = -1400 + 2500

Combine like terms: -1400 + 2500 = 1100
2500 + -100x + x2 = 1100

Factor a perfect square on the left side:
(x + -50)(x + -50) = 1100

Calculate the square root of the right side: 33.166247904

Break this problem into two subproblems by setting 
(x + -50) equal to 33.166247904 and -33.166247904.

Subproblem 1

x + -50 = 33.166247904 Simplifying x + -50 = 33.166247904 Reorder the terms: -50 + x = 33.166247904 Solving -50 + x = 33.166247904 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 = 33.166247904 + 50 Combine like terms: -50 + 50 = 0 0 + x = 33.166247904 + 50 x = 33.166247904 + 50 Combine like terms: 33.166247904 + 50 = 83.166247904 x = 83.166247904 Simplifying x = 83.166247904

Subproblem 2

x + -50 = -33.166247904 Simplifying x + -50 = -33.166247904 Reorder the terms: -50 + x = -33.166247904 Solving -50 + x = -33.166247904 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 = -33.166247904 + 50 Combine like terms: -50 + 50 = 0 0 + x = -33.166247904 + 50 x = -33.166247904 + 50 Combine like terms: -33.166247904 + 50 = 16.833752096 x = 16.833752096 Simplifying x = 16.833752096

Solution

The solution to the problem is based on the solutions from the subproblems. x = {83.166247904, 16.833752096}

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