8x^2-19x-648=0

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Solution for 8x^2-19x-648=0 equation:


Simplifying
8x2 + -19x + -648 = 0

Reorder the terms:
-648 + -19x + 8x2 = 0

Solving
-648 + -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'.
-81 + -2.375x + x2 = 0

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + -2.375x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + -2.375x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -2.375x + x2 = 0 + 81
-2.375x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
-2.375x + x2 = 81

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 = 81 + 1.41015625

Reorder the terms:
1.41015625 + -2.375x + x2 = 81 + 1.41015625

Combine like terms: 81 + 1.41015625 = 82.41015625
1.41015625 + -2.375x + x2 = 82.41015625

Factor a perfect square on the left side:
(x + -1.1875)(x + -1.1875) = 82.41015625

Calculate the square root of the right side: 9.078003979

Break this problem into two subproblems by setting 
(x + -1.1875) equal to 9.078003979 and -9.078003979.

Subproblem 1

x + -1.1875 = 9.078003979 Simplifying x + -1.1875 = 9.078003979 Reorder the terms: -1.1875 + x = 9.078003979 Solving -1.1875 + x = 9.078003979 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 = 9.078003979 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + x = 9.078003979 + 1.1875 x = 9.078003979 + 1.1875 Combine like terms: 9.078003979 + 1.1875 = 10.265503979 x = 10.265503979 Simplifying x = 10.265503979

Subproblem 2

x + -1.1875 = -9.078003979 Simplifying x + -1.1875 = -9.078003979 Reorder the terms: -1.1875 + x = -9.078003979 Solving -1.1875 + x = -9.078003979 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 = -9.078003979 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + x = -9.078003979 + 1.1875 x = -9.078003979 + 1.1875 Combine like terms: -9.078003979 + 1.1875 = -7.890503979 x = -7.890503979 Simplifying x = -7.890503979

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.265503979, -7.890503979}

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