4x^2-9x-6=8

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Solution for 4x^2-9x-6=8 equation:


Simplifying
4x2 + -9x + -6 = 8

Reorder the terms:
-6 + -9x + 4x2 = 8

Solving
-6 + -9x + 4x2 = 8

Solving for variable 'x'.

Reorder the terms:
-6 + -8 + -9x + 4x2 = 8 + -8

Combine like terms: -6 + -8 = -14
-14 + -9x + 4x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-14 + -9x + 4x2 = 0

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

Divide each side by '4'.
-3.5 + -2.25x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -2.25x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -2.25x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -2.25x + x2 = 0 + 3.5
-2.25x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-2.25x + x2 = 3.5

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = 3.5 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = 3.5 + 1.265625

Combine like terms: 3.5 + 1.265625 = 4.765625
1.265625 + -2.25x + x2 = 4.765625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 4.765625

Calculate the square root of the right side: 2.18303115

Break this problem into two subproblems by setting 
(x + -1.125) equal to 2.18303115 and -2.18303115.

Subproblem 1

x + -1.125 = 2.18303115 Simplifying x + -1.125 = 2.18303115 Reorder the terms: -1.125 + x = 2.18303115 Solving -1.125 + x = 2.18303115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 2.18303115 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 2.18303115 + 1.125 x = 2.18303115 + 1.125 Combine like terms: 2.18303115 + 1.125 = 3.30803115 x = 3.30803115 Simplifying x = 3.30803115

Subproblem 2

x + -1.125 = -2.18303115 Simplifying x + -1.125 = -2.18303115 Reorder the terms: -1.125 + x = -2.18303115 Solving -1.125 + x = -2.18303115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -2.18303115 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -2.18303115 + 1.125 x = -2.18303115 + 1.125 Combine like terms: -2.18303115 + 1.125 = -1.05803115 x = -1.05803115 Simplifying x = -1.05803115

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.30803115, -1.05803115}

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