4x^2-61x+173=0

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Solution for 4x^2-61x+173=0 equation:


Simplifying
4x2 + -61x + 173 = 0

Reorder the terms:
173 + -61x + 4x2 = 0

Solving
173 + -61x + 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'.
43.25 + -15.25x + x2 = 0

Move the constant term to the right:

Add '-43.25' to each side of the equation.
43.25 + -15.25x + -43.25 + x2 = 0 + -43.25

Reorder the terms:
43.25 + -43.25 + -15.25x + x2 = 0 + -43.25

Combine like terms: 43.25 + -43.25 = 0.00
0.00 + -15.25x + x2 = 0 + -43.25
-15.25x + x2 = 0 + -43.25

Combine like terms: 0 + -43.25 = -43.25
-15.25x + x2 = -43.25

The x term is -15.25x.  Take half its coefficient (-7.625).
Square it (58.140625) and add it to both sides.

Add '58.140625' to each side of the equation.
-15.25x + 58.140625 + x2 = -43.25 + 58.140625

Reorder the terms:
58.140625 + -15.25x + x2 = -43.25 + 58.140625

Combine like terms: -43.25 + 58.140625 = 14.890625
58.140625 + -15.25x + x2 = 14.890625

Factor a perfect square on the left side:
(x + -7.625)(x + -7.625) = 14.890625

Calculate the square root of the right side: 3.85883726

Break this problem into two subproblems by setting 
(x + -7.625) equal to 3.85883726 and -3.85883726.

Subproblem 1

x + -7.625 = 3.85883726 Simplifying x + -7.625 = 3.85883726 Reorder the terms: -7.625 + x = 3.85883726 Solving -7.625 + x = 3.85883726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.625' to each side of the equation. -7.625 + 7.625 + x = 3.85883726 + 7.625 Combine like terms: -7.625 + 7.625 = 0.000 0.000 + x = 3.85883726 + 7.625 x = 3.85883726 + 7.625 Combine like terms: 3.85883726 + 7.625 = 11.48383726 x = 11.48383726 Simplifying x = 11.48383726

Subproblem 2

x + -7.625 = -3.85883726 Simplifying x + -7.625 = -3.85883726 Reorder the terms: -7.625 + x = -3.85883726 Solving -7.625 + x = -3.85883726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.625' to each side of the equation. -7.625 + 7.625 + x = -3.85883726 + 7.625 Combine like terms: -7.625 + 7.625 = 0.000 0.000 + x = -3.85883726 + 7.625 x = -3.85883726 + 7.625 Combine like terms: -3.85883726 + 7.625 = 3.76616274 x = 3.76616274 Simplifying x = 3.76616274

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.48383726, 3.76616274}

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