4x^2-85x+357=0

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Solution for 4x^2-85x+357=0 equation:


Simplifying
4x2 + -85x + 357 = 0

Reorder the terms:
357 + -85x + 4x2 = 0

Solving
357 + -85x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
89.25 + -21.25x + x2 = 0

Move the constant term to the right:

Add '-89.25' to each side of the equation.
89.25 + -21.25x + -89.25 + x2 = 0 + -89.25

Reorder the terms:
89.25 + -89.25 + -21.25x + x2 = 0 + -89.25

Combine like terms: 89.25 + -89.25 = 0.00
0.00 + -21.25x + x2 = 0 + -89.25
-21.25x + x2 = 0 + -89.25

Combine like terms: 0 + -89.25 = -89.25
-21.25x + x2 = -89.25

The x term is -21.25x.  Take half its coefficient (-10.625).
Square it (112.890625) and add it to both sides.

Add '112.890625' to each side of the equation.
-21.25x + 112.890625 + x2 = -89.25 + 112.890625

Reorder the terms:
112.890625 + -21.25x + x2 = -89.25 + 112.890625

Combine like terms: -89.25 + 112.890625 = 23.640625
112.890625 + -21.25x + x2 = 23.640625

Factor a perfect square on the left side:
(x + -10.625)(x + -10.625) = 23.640625

Calculate the square root of the right side: 4.862162585

Break this problem into two subproblems by setting 
(x + -10.625) equal to 4.862162585 and -4.862162585.

Subproblem 1

x + -10.625 = 4.862162585 Simplifying x + -10.625 = 4.862162585 Reorder the terms: -10.625 + x = 4.862162585 Solving -10.625 + x = 4.862162585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.625' to each side of the equation. -10.625 + 10.625 + x = 4.862162585 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + x = 4.862162585 + 10.625 x = 4.862162585 + 10.625 Combine like terms: 4.862162585 + 10.625 = 15.487162585 x = 15.487162585 Simplifying x = 15.487162585

Subproblem 2

x + -10.625 = -4.862162585 Simplifying x + -10.625 = -4.862162585 Reorder the terms: -10.625 + x = -4.862162585 Solving -10.625 + x = -4.862162585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.625' to each side of the equation. -10.625 + 10.625 + x = -4.862162585 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + x = -4.862162585 + 10.625 x = -4.862162585 + 10.625 Combine like terms: -4.862162585 + 10.625 = 5.762837415 x = 5.762837415 Simplifying x = 5.762837415

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.487162585, 5.762837415}

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