2x^2-16x=-1

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Solution for 2x^2-16x=-1 equation:


Simplifying
2x2 + -16x = -1

Reorder the terms:
-16x + 2x2 = -1

Solving
-16x + 2x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + -16x + 2x2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -16x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
0.5 + -8x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -8x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -8x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -8x + x2 = 0 + -0.5
-8x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-8x + x2 = -0.5

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -0.5 + 16

Reorder the terms:
16 + -8x + x2 = -0.5 + 16

Combine like terms: -0.5 + 16 = 15.5
16 + -8x + x2 = 15.5

Factor a perfect square on the left side:
(x + -4)(x + -4) = 15.5

Calculate the square root of the right side: 3.937003937

Break this problem into two subproblems by setting 
(x + -4) equal to 3.937003937 and -3.937003937.

Subproblem 1

x + -4 = 3.937003937 Simplifying x + -4 = 3.937003937 Reorder the terms: -4 + x = 3.937003937 Solving -4 + x = 3.937003937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.937003937 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.937003937 + 4 x = 3.937003937 + 4 Combine like terms: 3.937003937 + 4 = 7.937003937 x = 7.937003937 Simplifying x = 7.937003937

Subproblem 2

x + -4 = -3.937003937 Simplifying x + -4 = -3.937003937 Reorder the terms: -4 + x = -3.937003937 Solving -4 + x = -3.937003937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.937003937 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.937003937 + 4 x = -3.937003937 + 4 Combine like terms: -3.937003937 + 4 = 0.062996063 x = 0.062996063 Simplifying x = 0.062996063

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.937003937, 0.062996063}

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