4x^2+17x+3=0

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Solution for 4x^2+17x+3=0 equation:


Simplifying
4x2 + 17x + 3 = 0

Reorder the terms:
3 + 17x + 4x2 = 0

Solving
3 + 17x + 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'.
0.75 + 4.25x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 4.25x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 4.25x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 4.25x + x2 = 0 + -0.75
4.25x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
4.25x + x2 = -0.75

The x term is 4.25x.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25x + 4.515625 + x2 = -0.75 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = -0.75 + 4.515625

Combine like terms: -0.75 + 4.515625 = 3.765625
4.515625 + 4.25x + x2 = 3.765625

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = 3.765625

Calculate the square root of the right side: 1.940521837

Break this problem into two subproblems by setting 
(x + 2.125) equal to 1.940521837 and -1.940521837.

Subproblem 1

x + 2.125 = 1.940521837 Simplifying x + 2.125 = 1.940521837 Reorder the terms: 2.125 + x = 1.940521837 Solving 2.125 + x = 1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 1.940521837 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 1.940521837 + -2.125 x = 1.940521837 + -2.125 Combine like terms: 1.940521837 + -2.125 = -0.184478163 x = -0.184478163 Simplifying x = -0.184478163

Subproblem 2

x + 2.125 = -1.940521837 Simplifying x + 2.125 = -1.940521837 Reorder the terms: 2.125 + x = -1.940521837 Solving 2.125 + x = -1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -1.940521837 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -1.940521837 + -2.125 x = -1.940521837 + -2.125 Combine like terms: -1.940521837 + -2.125 = -4.065521837 x = -4.065521837 Simplifying x = -4.065521837

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.184478163, -4.065521837}

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