8x^2-19x-6=

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Solution for 8x^2-19x-6= equation:


Simplifying
8x2 + -19x + -6 = 0

Reorder the terms:
-6 + -19x + 8x2 = 0

Solving
-6 + -19x + 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'.
-0.75 + -2.375x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -2.375x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -2.375x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -2.375x + x2 = 0 + 0.75
-2.375x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-2.375x + x2 = 0.75

The x term is -2.375x.  Take half its coefficient (-1.1875).
Square it (1.41015625) and add it to both sides.

Add '1.41015625' to each side of the equation.
-2.375x + 1.41015625 + x2 = 0.75 + 1.41015625

Reorder the terms:
1.41015625 + -2.375x + x2 = 0.75 + 1.41015625

Combine like terms: 0.75 + 1.41015625 = 2.16015625
1.41015625 + -2.375x + x2 = 2.16015625

Factor a perfect square on the left side:
(x + -1.1875)(x + -1.1875) = 2.16015625

Calculate the square root of the right side: 1.469747002

Break this problem into two subproblems by setting 
(x + -1.1875) equal to 1.469747002 and -1.469747002.

Subproblem 1

x + -1.1875 = 1.469747002 Simplifying x + -1.1875 = 1.469747002 Reorder the terms: -1.1875 + x = 1.469747002 Solving -1.1875 + x = 1.469747002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + x = 1.469747002 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + x = 1.469747002 + 1.1875 x = 1.469747002 + 1.1875 Combine like terms: 1.469747002 + 1.1875 = 2.657247002 x = 2.657247002 Simplifying x = 2.657247002

Subproblem 2

x + -1.1875 = -1.469747002 Simplifying x + -1.1875 = -1.469747002 Reorder the terms: -1.1875 + x = -1.469747002 Solving -1.1875 + x = -1.469747002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + x = -1.469747002 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + x = -1.469747002 + 1.1875 x = -1.469747002 + 1.1875 Combine like terms: -1.469747002 + 1.1875 = -0.282247002 x = -0.282247002 Simplifying x = -0.282247002

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.657247002, -0.282247002}

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