4x-1*8x^2+34x-1=

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Solution for 4x-1*8x^2+34x-1= equation:


Simplifying
4x + -1 * 8x2 + 34x + -1 = 0

Multiply -1 * 8
4x + -8x2 + 34x + -1 = 0

Reorder the terms:
-1 + 4x + 34x + -8x2 = 0

Combine like terms: 4x + 34x = 38x
-1 + 38x + -8x2 = 0

Solving
-1 + 38x + -8x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
0.125 + -4.75x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -4.75x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -4.75x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -4.75x + x2 = 0 + -0.125
-4.75x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-4.75x + x2 = -0.125

The x term is -4.75x.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75x + 5.640625 + x2 = -0.125 + 5.640625

Reorder the terms:
5.640625 + -4.75x + x2 = -0.125 + 5.640625

Combine like terms: -0.125 + 5.640625 = 5.515625
5.640625 + -4.75x + x2 = 5.515625

Factor a perfect square on the left side:
(x + -2.375)(x + -2.375) = 5.515625

Calculate the square root of the right side: 2.348536779

Break this problem into two subproblems by setting 
(x + -2.375) equal to 2.348536779 and -2.348536779.

Subproblem 1

x + -2.375 = 2.348536779 Simplifying x + -2.375 = 2.348536779 Reorder the terms: -2.375 + x = 2.348536779 Solving -2.375 + x = 2.348536779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 2.348536779 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 2.348536779 + 2.375 x = 2.348536779 + 2.375 Combine like terms: 2.348536779 + 2.375 = 4.723536779 x = 4.723536779 Simplifying x = 4.723536779

Subproblem 2

x + -2.375 = -2.348536779 Simplifying x + -2.375 = -2.348536779 Reorder the terms: -2.375 + x = -2.348536779 Solving -2.375 + x = -2.348536779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -2.348536779 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -2.348536779 + 2.375 x = -2.348536779 + 2.375 Combine like terms: -2.348536779 + 2.375 = 0.026463221 x = 0.026463221 Simplifying x = 0.026463221

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.723536779, 0.026463221}

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