4x^2-17x=4

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


Simplifying
4x2 + -17x = 4

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

Solving
-17x + 4x2 = 4

Solving for variable 'x'.

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

Combine like terms: 4 + -4 = 0
-4 + -17x + 4x2 = 0

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 = 4.473536779 x = 4.473536779 Simplifying x = 4.473536779

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 = -0.223536779 x = -0.223536779 Simplifying x = -0.223536779

Solution

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

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