-16x^2+26x+100=0

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Solution for -16x^2+26x+100=0 equation: 


Simplifying
-16x2 + 26x + 100 = 0

Reorder the terms:
100 + 26x + -16x2 = 0

Solving
100 + 26x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(50 + 13x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(50 + 13x + -8x2)' equal to zero and attempt to solve:

Simplifying
50 + 13x + -8x2 = 0

Solving
50 + 13x + -8x2 = 0

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

Divide each side by '-8'.
-6.25 + -1.625x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + -1.625x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + -1.625x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + -1.625x + x2 = 0 + 6.25
-1.625x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
-1.625x + x2 = 6.25

The x term is -1.625x.  Take half its coefficient (-0.8125).
Square it (0.66015625) and add it to both sides.

Add '0.66015625' to each side of the equation.
-1.625x + 0.66015625 + x2 = 6.25 + 0.66015625

Reorder the terms:
0.66015625 + -1.625x + x2 = 6.25 + 0.66015625

Combine like terms: 6.25 + 0.66015625 = 6.91015625
0.66015625 + -1.625x + x2 = 6.91015625

Factor a perfect square on the left side:
(x + -0.8125)(x + -0.8125) = 6.91015625

Calculate the square root of the right side: 2.628717606

Break this problem into two subproblems by setting 
(x + -0.8125) equal to 2.628717606 and -2.628717606.


Subproblem 1
x + -0.8125 = 2.628717606

Simplifying
x + -0.8125 = 2.628717606

Reorder the terms:
-0.8125 + x = 2.628717606

Solving
-0.8125 + x = 2.628717606

Solving for variable 'x'.

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

Add '0.8125' to each side of the equation.
-0.8125 + 0.8125 + x = 2.628717606 + 0.8125

Combine like terms: -0.8125 + 0.8125 = 0.0000
0.0000 + x = 2.628717606 + 0.8125
x = 2.628717606 + 0.8125

Combine like terms: 2.628717606 + 0.8125 = 3.441217606
x = 3.441217606

Simplifying
x = 3.441217606


Subproblem 2
x + -0.8125 = -2.628717606

Simplifying
x + -0.8125 = -2.628717606

Reorder the terms:
-0.8125 + x = -2.628717606

Solving
-0.8125 + x = -2.628717606

Solving for variable 'x'.

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

Add '0.8125' to each side of the equation.
-0.8125 + 0.8125 + x = -2.628717606 + 0.8125

Combine like terms: -0.8125 + 0.8125 = 0.0000
0.0000 + x = -2.628717606 + 0.8125
x = -2.628717606 + 0.8125

Combine like terms: -2.628717606 + 0.8125 = -1.816217606
x = -1.816217606

Simplifying
x = -1.816217606


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.441217606, -1.816217606}
Solution
x = {3.441217606, -1.816217606}

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