-16x^2+16x+98=0

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Solution for -16x^2+16x+98=0 equation: 


Simplifying
-16x2 + 16x + 98 = 0

Reorder the terms:
98 + 16x + -16x2 = 0

Solving
98 + 16x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(49 + 8x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(49 + 8x + -8x2)' equal to zero and attempt to solve:

Simplifying
49 + 8x + -8x2 = 0

Solving
49 + 8x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-6.125 + -1x + x2 = 0

Move the constant term to the right:

Add '6.125' to each side of the equation.
-6.125 + -1x + 6.125 + x2 = 0 + 6.125

Reorder the terms:
-6.125 + 6.125 + -1x + x2 = 0 + 6.125

Combine like terms: -6.125 + 6.125 = 0.000
0.000 + -1x + x2 = 0 + 6.125
-1x + x2 = 0 + 6.125

Combine like terms: 0 + 6.125 = 6.125
-1x + x2 = 6.125

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 6.125 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 6.125 + 0.25

Combine like terms: 6.125 + 0.25 = 6.375
0.25 + -1x + x2 = 6.375

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 6.375

Calculate the square root of the right side: 2.524876235

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.524876235 and -2.524876235.


Subproblem 1
x + -0.5 = 2.524876235

Simplifying
x + -0.5 = 2.524876235

Reorder the terms:
-0.5 + x = 2.524876235

Solving
-0.5 + x = 2.524876235

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 2.524876235 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 2.524876235 + 0.5
x = 2.524876235 + 0.5

Combine like terms: 2.524876235 + 0.5 = 3.024876235
x = 3.024876235

Simplifying
x = 3.024876235


Subproblem 2
x + -0.5 = -2.524876235

Simplifying
x + -0.5 = -2.524876235

Reorder the terms:
-0.5 + x = -2.524876235

Solving
-0.5 + x = -2.524876235

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -2.524876235 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -2.524876235 + 0.5
x = -2.524876235 + 0.5

Combine like terms: -2.524876235 + 0.5 = -2.024876235
x = -2.024876235

Simplifying
x = -2.024876235


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.024876235, -2.024876235}
Solution
x = {3.024876235, -2.024876235}

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