-16X^2+35X+5=0

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Solution for -16X^2+35X+5=0 equation:


Simplifying
-16X2 + 35X + 5 = 0

Reorder the terms:
5 + 35X + -16X2 = 0

Solving
5 + 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'.
-0.3125 + -2.1875X + X2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -2.1875X + 0.3125 + X2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -2.1875X + X2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -2.1875X + X2 = 0 + 0.3125
-2.1875X + X2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-2.1875X + X2 = 0.3125

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 = 0.3125 + 1.196289063

Reorder the terms:
1.196289063 + -2.1875X + X2 = 0.3125 + 1.196289063

Combine like terms: 0.3125 + 1.196289063 = 1.508789063
1.196289063 + -2.1875X + X2 = 1.508789063

Factor a perfect square on the left side:
(X + -1.09375)(X + -1.09375) = 1.508789063

Calculate the square root of the right side: 1.228327751

Break this problem into two subproblems by setting 
(X + -1.09375) equal to 1.228327751 and -1.228327751.

Subproblem 1

X + -1.09375 = 1.228327751 Simplifying X + -1.09375 = 1.228327751 Reorder the terms: -1.09375 + X = 1.228327751 Solving -1.09375 + X = 1.228327751 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 = 1.228327751 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + X = 1.228327751 + 1.09375 X = 1.228327751 + 1.09375 Combine like terms: 1.228327751 + 1.09375 = 2.322077751 X = 2.322077751 Simplifying X = 2.322077751

Subproblem 2

X + -1.09375 = -1.228327751 Simplifying X + -1.09375 = -1.228327751 Reorder the terms: -1.09375 + X = -1.228327751 Solving -1.09375 + X = -1.228327751 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 = -1.228327751 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + X = -1.228327751 + 1.09375 X = -1.228327751 + 1.09375 Combine like terms: -1.228327751 + 1.09375 = -0.134577751 X = -0.134577751 Simplifying X = -0.134577751

Solution

The solution to the problem is based on the solutions from the subproblems. X = {2.322077751, -0.134577751}

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