-16x^2+69x+26=0

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Solution for -16x^2+69x+26=0 equation: 


Simplifying
-16x2 + 69x + 26 = 0

Reorder the terms:
26 + 69x + -16x2 = 0

Solving
26 + 69x + -16x2 = 0

Solving for variable 'x'.

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

Divide each side by '-16'.
-1.625 + -4.3125x + x2 = 0

Move the constant term to the right:

Add '1.625' to each side of the equation.
-1.625 + -4.3125x + 1.625 + x2 = 0 + 1.625

Reorder the terms:
-1.625 + 1.625 + -4.3125x + x2 = 0 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + -4.3125x + x2 = 0 + 1.625
-4.3125x + x2 = 0 + 1.625

Combine like terms: 0 + 1.625 = 1.625
-4.3125x + x2 = 1.625

The x term is -4.3125x.  Take half its coefficient (-2.15625).
Square it (4.649414063) and add it to both sides.

Add '4.649414063' to each side of the equation.
-4.3125x + 4.649414063 + x2 = 1.625 + 4.649414063

Reorder the terms:
4.649414063 + -4.3125x + x2 = 1.625 + 4.649414063

Combine like terms: 1.625 + 4.649414063 = 6.274414063
4.649414063 + -4.3125x + x2 = 6.274414063

Factor a perfect square on the left side:
(x + -2.15625)(x + -2.15625) = 6.274414063

Calculate the square root of the right side: 2.504878054

Break this problem into two subproblems by setting 
(x + -2.15625) equal to 2.504878054 and -2.504878054.


Subproblem 1
x + -2.15625 = 2.504878054

Simplifying
x + -2.15625 = 2.504878054

Reorder the terms:
-2.15625 + x = 2.504878054

Solving
-2.15625 + x = 2.504878054

Solving for variable 'x'.

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

Add '2.15625' to each side of the equation.
-2.15625 + 2.15625 + x = 2.504878054 + 2.15625

Combine like terms: -2.15625 + 2.15625 = 0.00000
0.00000 + x = 2.504878054 + 2.15625
x = 2.504878054 + 2.15625

Combine like terms: 2.504878054 + 2.15625 = 4.661128054
x = 4.661128054

Simplifying
x = 4.661128054


Subproblem 2
x + -2.15625 = -2.504878054

Simplifying
x + -2.15625 = -2.504878054

Reorder the terms:
-2.15625 + x = -2.504878054

Solving
-2.15625 + x = -2.504878054

Solving for variable 'x'.

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

Add '2.15625' to each side of the equation.
-2.15625 + 2.15625 + x = -2.504878054 + 2.15625

Combine like terms: -2.15625 + 2.15625 = 0.00000
0.00000 + x = -2.504878054 + 2.15625
x = -2.504878054 + 2.15625

Combine like terms: -2.504878054 + 2.15625 = -0.348628054
x = -0.348628054

Simplifying
x = -0.348628054


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.661128054, -0.348628054}

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