16x^2-2x-8=21

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Solution for 16x^2-2x-8=21 equation:


Simplifying
16x2 + -2x + -8 = 21

Reorder the terms:
-8 + -2x + 16x2 = 21

Solving
-8 + -2x + 16x2 = 21

Solving for variable 'x'.

Reorder the terms:
-8 + -21 + -2x + 16x2 = 21 + -21

Combine like terms: -8 + -21 = -29
-29 + -2x + 16x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-29 + -2x + 16x2 = 0

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

Divide each side by '16'.
-1.8125 + -0.125x + x2 = 0

Move the constant term to the right:

Add '1.8125' to each side of the equation.
-1.8125 + -0.125x + 1.8125 + x2 = 0 + 1.8125

Reorder the terms:
-1.8125 + 1.8125 + -0.125x + x2 = 0 + 1.8125

Combine like terms: -1.8125 + 1.8125 = 0.0000
0.0000 + -0.125x + x2 = 0 + 1.8125
-0.125x + x2 = 0 + 1.8125

Combine like terms: 0 + 1.8125 = 1.8125
-0.125x + x2 = 1.8125

The x term is -0.125x.  Take half its coefficient (-0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
-0.125x + 0.00390625 + x2 = 1.8125 + 0.00390625

Reorder the terms:
0.00390625 + -0.125x + x2 = 1.8125 + 0.00390625

Combine like terms: 1.8125 + 0.00390625 = 1.81640625
0.00390625 + -0.125x + x2 = 1.81640625

Factor a perfect square on the left side:
(x + -0.0625)(x + -0.0625) = 1.81640625

Calculate the square root of the right side: 1.347741166

Break this problem into two subproblems by setting 
(x + -0.0625) equal to 1.347741166 and -1.347741166.

Subproblem 1

x + -0.0625 = 1.347741166 Simplifying x + -0.0625 = 1.347741166 Reorder the terms: -0.0625 + x = 1.347741166 Solving -0.0625 + x = 1.347741166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 1.347741166 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 1.347741166 + 0.0625 x = 1.347741166 + 0.0625 Combine like terms: 1.347741166 + 0.0625 = 1.410241166 x = 1.410241166 Simplifying x = 1.410241166

Subproblem 2

x + -0.0625 = -1.347741166 Simplifying x + -0.0625 = -1.347741166 Reorder the terms: -0.0625 + x = -1.347741166 Solving -0.0625 + x = -1.347741166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -1.347741166 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -1.347741166 + 0.0625 x = -1.347741166 + 0.0625 Combine like terms: -1.347741166 + 0.0625 = -1.285241166 x = -1.285241166 Simplifying x = -1.285241166

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.410241166, -1.285241166}

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