4x^2+17x-4=0

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


Simplifying
4x2 + 17x + -4 = 0

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

Solving
-4 + 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'.
-1 + 4.25x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 4.25x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 4.25x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4.25x + x2 = 0 + 1
4.25x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
4.25x + x2 = 1

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 = 1 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = 1 + 4.515625

Combine like terms: 1 + 4.515625 = 5.515625
4.515625 + 4.25x + x2 = 5.515625

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = 5.515625

Calculate the square root of the right side: 2.348536779

Break this problem into two subproblems by setting 
(x + 2.125) equal to 2.348536779 and -2.348536779.

Subproblem 1

x + 2.125 = 2.348536779 Simplifying x + 2.125 = 2.348536779 Reorder the terms: 2.125 + x = 2.348536779 Solving 2.125 + x = 2.348536779 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 = 2.348536779 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 2.348536779 + -2.125 x = 2.348536779 + -2.125 Combine like terms: 2.348536779 + -2.125 = 0.223536779 x = 0.223536779 Simplifying x = 0.223536779

Subproblem 2

x + 2.125 = -2.348536779 Simplifying x + 2.125 = -2.348536779 Reorder the terms: 2.125 + x = -2.348536779 Solving 2.125 + x = -2.348536779 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 = -2.348536779 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -2.348536779 + -2.125 x = -2.348536779 + -2.125 Combine like terms: -2.348536779 + -2.125 = -4.473536779 x = -4.473536779 Simplifying x = -4.473536779

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.223536779, -4.473536779}

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