0=16x^2-35x-4

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Solution for 0=16x^2-35x-4 equation:


Simplifying
0 = 16x2 + -35x + -4

Reorder the terms:
0 = -4 + -35x + 16x2

Solving
0 = -4 + -35x + 16x2

Solving for variable 'x'.

Combine like terms: 0 + 4 = 4
4 + 35x + -16x2 = -4 + -35x + 16x2 + 4 + 35x + -16x2

Reorder the terms:
4 + 35x + -16x2 = -4 + 4 + -35x + 35x + 16x2 + -16x2

Combine like terms: -4 + 4 = 0
4 + 35x + -16x2 = 0 + -35x + 35x + 16x2 + -16x2
4 + 35x + -16x2 = -35x + 35x + 16x2 + -16x2

Combine like terms: -35x + 35x = 0
4 + 35x + -16x2 = 0 + 16x2 + -16x2
4 + 35x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
4 + 35x + -16x2 = 0

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

Divide each side by '-16'.
-0.25 + -2.1875x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -2.1875x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -2.1875x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -2.1875x + x2 = 0 + 0.25
-2.1875x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-2.1875x + x2 = 0.25

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 = 0.25 + 1.196289063

Reorder the terms:
1.196289063 + -2.1875x + x2 = 0.25 + 1.196289063

Combine like terms: 0.25 + 1.196289063 = 1.446289063
1.196289063 + -2.1875x + x2 = 1.446289063

Factor a perfect square on the left side:
(x + -1.09375)(x + -1.09375) = 1.446289063

Calculate the square root of the right side: 1.202617588

Break this problem into two subproblems by setting 
(x + -1.09375) equal to 1.202617588 and -1.202617588.

Subproblem 1

x + -1.09375 = 1.202617588 Simplifying x + -1.09375 = 1.202617588 Reorder the terms: -1.09375 + x = 1.202617588 Solving -1.09375 + x = 1.202617588 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 = 1.202617588 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = 1.202617588 + 1.09375 x = 1.202617588 + 1.09375 Combine like terms: 1.202617588 + 1.09375 = 2.296367588 x = 2.296367588 Simplifying x = 2.296367588

Subproblem 2

x + -1.09375 = -1.202617588 Simplifying x + -1.09375 = -1.202617588 Reorder the terms: -1.09375 + x = -1.202617588 Solving -1.09375 + x = -1.202617588 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 = -1.202617588 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = -1.202617588 + 1.09375 x = -1.202617588 + 1.09375 Combine like terms: -1.202617588 + 1.09375 = -0.108867588 x = -0.108867588 Simplifying x = -0.108867588

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.296367588, -0.108867588}

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