4x^2+123x+172=0

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Solution for 4x^2+123x+172=0 equation:


Simplifying
4x2 + 123x + 172 = 0

Reorder the terms:
172 + 123x + 4x2 = 0

Solving
172 + 123x + 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 + 30.75x + x2 = 0

Move the constant term to the right:

Add '-43' to each side of the equation.
43 + 30.75x + -43 + x2 = 0 + -43

Reorder the terms:
43 + -43 + 30.75x + x2 = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 30.75x + x2 = 0 + -43
30.75x + x2 = 0 + -43

Combine like terms: 0 + -43 = -43
30.75x + x2 = -43

The x term is 30.75x.  Take half its coefficient (15.375).
Square it (236.390625) and add it to both sides.

Add '236.390625' to each side of the equation.
30.75x + 236.390625 + x2 = -43 + 236.390625

Reorder the terms:
236.390625 + 30.75x + x2 = -43 + 236.390625

Combine like terms: -43 + 236.390625 = 193.390625
236.390625 + 30.75x + x2 = 193.390625

Factor a perfect square on the left side:
(x + 15.375)(x + 15.375) = 193.390625

Calculate the square root of the right side: 13.906495784

Break this problem into two subproblems by setting 
(x + 15.375) equal to 13.906495784 and -13.906495784.

Subproblem 1

x + 15.375 = 13.906495784 Simplifying x + 15.375 = 13.906495784 Reorder the terms: 15.375 + x = 13.906495784 Solving 15.375 + x = 13.906495784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.375' to each side of the equation. 15.375 + -15.375 + x = 13.906495784 + -15.375 Combine like terms: 15.375 + -15.375 = 0.000 0.000 + x = 13.906495784 + -15.375 x = 13.906495784 + -15.375 Combine like terms: 13.906495784 + -15.375 = -1.468504216 x = -1.468504216 Simplifying x = -1.468504216

Subproblem 2

x + 15.375 = -13.906495784 Simplifying x + 15.375 = -13.906495784 Reorder the terms: 15.375 + x = -13.906495784 Solving 15.375 + x = -13.906495784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.375' to each side of the equation. 15.375 + -15.375 + x = -13.906495784 + -15.375 Combine like terms: 15.375 + -15.375 = 0.000 0.000 + x = -13.906495784 + -15.375 x = -13.906495784 + -15.375 Combine like terms: -13.906495784 + -15.375 = -29.281495784 x = -29.281495784 Simplifying x = -29.281495784

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.468504216, -29.281495784}

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