4x^2-x-16=

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Solution for 4x^2-x-16= equation:


Simplifying
4x2 + -1x + -16 = 0

Reorder the terms:
-16 + -1x + 4x2 = 0

Solving
-16 + -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'.
-4 + -0.25x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -0.25x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -0.25x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -0.25x + x2 = 0 + 4
-0.25x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-0.25x + x2 = 4

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 = 4 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 4 + 0.015625

Combine like terms: 4 + 0.015625 = 4.015625
0.015625 + -0.25x + x2 = 4.015625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 4.015625

Calculate the square root of the right side: 2.003902443

Break this problem into two subproblems by setting 
(x + -0.125) equal to 2.003902443 and -2.003902443.

Subproblem 1

x + -0.125 = 2.003902443 Simplifying x + -0.125 = 2.003902443 Reorder the terms: -0.125 + x = 2.003902443 Solving -0.125 + x = 2.003902443 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 = 2.003902443 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 2.003902443 + 0.125 x = 2.003902443 + 0.125 Combine like terms: 2.003902443 + 0.125 = 2.128902443 x = 2.128902443 Simplifying x = 2.128902443

Subproblem 2

x + -0.125 = -2.003902443 Simplifying x + -0.125 = -2.003902443 Reorder the terms: -0.125 + x = -2.003902443 Solving -0.125 + x = -2.003902443 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 = -2.003902443 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -2.003902443 + 0.125 x = -2.003902443 + 0.125 Combine like terms: -2.003902443 + 0.125 = -1.878902443 x = -1.878902443 Simplifying x = -1.878902443

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.128902443, -1.878902443}

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