-16x^2+98x-42=0

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Solution for -16x^2+98x-42=0 equation: 


Simplifying
-16x2 + 98x + -42 = 0

Reorder the terms:
-42 + 98x + -16x2 = 0

Solving
-42 + 98x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 49x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-21 + 49x + -8x2)' equal to zero and attempt to solve:

Simplifying
-21 + 49x + -8x2 = 0

Solving
-21 + 49x + -8x2 = 0

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

Divide each side by '-8'.
2.625 + -6.125x + x2 = 0

Move the constant term to the right:

Add '-2.625' to each side of the equation.
2.625 + -6.125x + -2.625 + x2 = 0 + -2.625

Reorder the terms:
2.625 + -2.625 + -6.125x + x2 = 0 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + -6.125x + x2 = 0 + -2.625
-6.125x + x2 = 0 + -2.625

Combine like terms: 0 + -2.625 = -2.625
-6.125x + x2 = -2.625

The x term is -6.125x.  Take half its coefficient (-3.0625).
Square it (9.37890625) and add it to both sides.

Add '9.37890625' to each side of the equation.
-6.125x + 9.37890625 + x2 = -2.625 + 9.37890625

Reorder the terms:
9.37890625 + -6.125x + x2 = -2.625 + 9.37890625

Combine like terms: -2.625 + 9.37890625 = 6.75390625
9.37890625 + -6.125x + x2 = 6.75390625

Factor a perfect square on the left side:
(x + -3.0625)(x + -3.0625) = 6.75390625

Calculate the square root of the right side: 2.598827861

Break this problem into two subproblems by setting 
(x + -3.0625) equal to 2.598827861 and -2.598827861.


Subproblem 1
x + -3.0625 = 2.598827861

Simplifying
x + -3.0625 = 2.598827861

Reorder the terms:
-3.0625 + x = 2.598827861

Solving
-3.0625 + x = 2.598827861

Solving for variable 'x'.

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

Add '3.0625' to each side of the equation.
-3.0625 + 3.0625 + x = 2.598827861 + 3.0625

Combine like terms: -3.0625 + 3.0625 = 0.0000
0.0000 + x = 2.598827861 + 3.0625
x = 2.598827861 + 3.0625

Combine like terms: 2.598827861 + 3.0625 = 5.661327861
x = 5.661327861

Simplifying
x = 5.661327861


Subproblem 2
x + -3.0625 = -2.598827861

Simplifying
x + -3.0625 = -2.598827861

Reorder the terms:
-3.0625 + x = -2.598827861

Solving
-3.0625 + x = -2.598827861

Solving for variable 'x'.

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

Add '3.0625' to each side of the equation.
-3.0625 + 3.0625 + x = -2.598827861 + 3.0625

Combine like terms: -3.0625 + 3.0625 = 0.0000
0.0000 + x = -2.598827861 + 3.0625
x = -2.598827861 + 3.0625

Combine like terms: -2.598827861 + 3.0625 = 0.463672139
x = 0.463672139

Simplifying
x = 0.463672139


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.661327861, 0.463672139}
Solution
x = {5.661327861, 0.463672139}

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