-16x^2+35x-18=0

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Solution for -16x^2+35x-18=0 equation: 


Simplifying
-16x2 + 35x + -18 = 0

Reorder the terms:
-18 + 35x + -16x2 = 0

Solving
-18 + 35x + -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'.
1.125 + -2.1875x + x2 = 0

Move the constant term to the right:

Add '-1.125' to each side of the equation.
1.125 + -2.1875x + -1.125 + x2 = 0 + -1.125

Reorder the terms:
1.125 + -1.125 + -2.1875x + x2 = 0 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + -2.1875x + x2 = 0 + -1.125
-2.1875x + x2 = 0 + -1.125

Combine like terms: 0 + -1.125 = -1.125
-2.1875x + x2 = -1.125

The x term is -2.1875x.  Take half its coefficient (-1.09375).
Square it (1.196289063) and add it to both sides.

Add '1.196289063' to each side of the equation.
-2.1875x + 1.196289063 + x2 = -1.125 + 1.196289063

Reorder the terms:
1.196289063 + -2.1875x + x2 = -1.125 + 1.196289063

Combine like terms: -1.125 + 1.196289063 = 0.071289063
1.196289063 + -2.1875x + x2 = 0.071289063

Factor a perfect square on the left side:
(x + -1.09375)(x + -1.09375) = 0.071289063

Calculate the square root of the right side: 0.267000118

Break this problem into two subproblems by setting 
(x + -1.09375) equal to 0.267000118 and -0.267000118.


Subproblem 1
x + -1.09375 = 0.267000118

Simplifying
x + -1.09375 = 0.267000118

Reorder the terms:
-1.09375 + x = 0.267000118

Solving
-1.09375 + x = 0.267000118

Solving for variable 'x'.

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

Add '1.09375' to each side of the equation.
-1.09375 + 1.09375 + x = 0.267000118 + 1.09375

Combine like terms: -1.09375 + 1.09375 = 0.00000
0.00000 + x = 0.267000118 + 1.09375
x = 0.267000118 + 1.09375

Combine like terms: 0.267000118 + 1.09375 = 1.360750118
x = 1.360750118

Simplifying
x = 1.360750118


Subproblem 2
x + -1.09375 = -0.267000118

Simplifying
x + -1.09375 = -0.267000118

Reorder the terms:
-1.09375 + x = -0.267000118

Solving
-1.09375 + x = -0.267000118

Solving for variable 'x'.

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

Add '1.09375' to each side of the equation.
-1.09375 + 1.09375 + x = -0.267000118 + 1.09375

Combine like terms: -1.09375 + 1.09375 = 0.00000
0.00000 + x = -0.267000118 + 1.09375
x = -0.267000118 + 1.09375

Combine like terms: -0.267000118 + 1.09375 = 0.826749882
x = 0.826749882

Simplifying
x = 0.826749882


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.360750118, 0.826749882}

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