x^2-190x+4465=0

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Solution for x^2-190x+4465=0 equation:


Simplifying
x2 + -190x + 4465 = 0

Reorder the terms:
4465 + -190x + x2 = 0

Solving
4465 + -190x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4465' to each side of the equation.
4465 + -190x + -4465 + x2 = 0 + -4465

Reorder the terms:
4465 + -4465 + -190x + x2 = 0 + -4465

Combine like terms: 4465 + -4465 = 0
0 + -190x + x2 = 0 + -4465
-190x + x2 = 0 + -4465

Combine like terms: 0 + -4465 = -4465
-190x + x2 = -4465

The x term is -190x.  Take half its coefficient (-95).
Square it (9025) and add it to both sides.

Add '9025' to each side of the equation.
-190x + 9025 + x2 = -4465 + 9025

Reorder the terms:
9025 + -190x + x2 = -4465 + 9025

Combine like terms: -4465 + 9025 = 4560
9025 + -190x + x2 = 4560

Factor a perfect square on the left side:
(x + -95)(x + -95) = 4560

Calculate the square root of the right side: 67.527772065

Break this problem into two subproblems by setting 
(x + -95) equal to 67.527772065 and -67.527772065.

Subproblem 1

x + -95 = 67.527772065 Simplifying x + -95 = 67.527772065 Reorder the terms: -95 + x = 67.527772065 Solving -95 + x = 67.527772065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '95' to each side of the equation. -95 + 95 + x = 67.527772065 + 95 Combine like terms: -95 + 95 = 0 0 + x = 67.527772065 + 95 x = 67.527772065 + 95 Combine like terms: 67.527772065 + 95 = 162.527772065 x = 162.527772065 Simplifying x = 162.527772065

Subproblem 2

x + -95 = -67.527772065 Simplifying x + -95 = -67.527772065 Reorder the terms: -95 + x = -67.527772065 Solving -95 + x = -67.527772065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '95' to each side of the equation. -95 + 95 + x = -67.527772065 + 95 Combine like terms: -95 + 95 = 0 0 + x = -67.527772065 + 95 x = -67.527772065 + 95 Combine like terms: -67.527772065 + 95 = 27.472227935 x = 27.472227935 Simplifying x = 27.472227935

Solution

The solution to the problem is based on the solutions from the subproblems. x = {162.527772065, 27.472227935}

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