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

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


Simplifying
-16x2 + 35x + 2 = 0

Reorder the terms:
2 + 35x + -16x2 = 0

Solving
2 + 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'.
-0.125 + -2.1875x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -2.1875x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -2.1875x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -2.1875x + x2 = 0 + 0.125
-2.1875x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-2.1875x + x2 = 0.125

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 = 0.125 + 1.196289063

Reorder the terms:
1.196289063 + -2.1875x + x2 = 0.125 + 1.196289063

Combine like terms: 0.125 + 1.196289063 = 1.321289063
1.196289063 + -2.1875x + x2 = 1.321289063

Factor a perfect square on the left side:
(x + -1.09375)(x + -1.09375) = 1.321289063

Calculate the square root of the right side: 1.149473385

Break this problem into two subproblems by setting 
(x + -1.09375) equal to 1.149473385 and -1.149473385.

Subproblem 1

x + -1.09375 = 1.149473385 Simplifying x + -1.09375 = 1.149473385 Reorder the terms: -1.09375 + x = 1.149473385 Solving -1.09375 + x = 1.149473385 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 = 1.149473385 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = 1.149473385 + 1.09375 x = 1.149473385 + 1.09375 Combine like terms: 1.149473385 + 1.09375 = 2.243223385 x = 2.243223385 Simplifying x = 2.243223385

Subproblem 2

x + -1.09375 = -1.149473385 Simplifying x + -1.09375 = -1.149473385 Reorder the terms: -1.09375 + x = -1.149473385 Solving -1.09375 + x = -1.149473385 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 = -1.149473385 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = -1.149473385 + 1.09375 x = -1.149473385 + 1.09375 Combine like terms: -1.149473385 + 1.09375 = -0.055723385 x = -0.055723385 Simplifying x = -0.055723385

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.243223385, -0.055723385}

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