4x^2-x-4=0

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


Simplifying
4x2 + -1x + -4 = 0

Reorder the terms:
-4 + -1x + 4x2 = 0

Solving
-4 + -1x + 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 + -0.25x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.25x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.25x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.25x + x2 = 0 + 1
-0.25x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.25x + x2 = 1

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 1 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 1 + 0.015625

Combine like terms: 1 + 0.015625 = 1.015625
0.015625 + -0.25x + x2 = 1.015625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(x + -0.125) equal to 1.007782219 and -1.007782219.

Subproblem 1

x + -0.125 = 1.007782219 Simplifying x + -0.125 = 1.007782219 Reorder the terms: -0.125 + x = 1.007782219 Solving -0.125 + x = 1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 1.007782219 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 1.007782219 + 0.125 x = 1.007782219 + 0.125 Combine like terms: 1.007782219 + 0.125 = 1.132782219 x = 1.132782219 Simplifying x = 1.132782219

Subproblem 2

x + -0.125 = -1.007782219 Simplifying x + -0.125 = -1.007782219 Reorder the terms: -0.125 + x = -1.007782219 Solving -0.125 + x = -1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -1.007782219 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -1.007782219 + 0.125 x = -1.007782219 + 0.125 Combine like terms: -1.007782219 + 0.125 = -0.882782219 x = -0.882782219 Simplifying x = -0.882782219

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.132782219, -0.882782219}

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