8x^2+9x-4=0

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Solution for 8x^2+9x-4=0 equation:


Simplifying
8x2 + 9x + -4 = 0

Reorder the terms:
-4 + 9x + 8x2 = 0

Solving
-4 + 9x + 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'.
-0.5 + 1.125x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 1.125x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 1.125x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 1.125x + x2 = 0 + 0.5
1.125x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
1.125x + x2 = 0.5

The x term is 1.125x.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125x + 0.31640625 + x2 = 0.5 + 0.31640625

Reorder the terms:
0.31640625 + 1.125x + x2 = 0.5 + 0.31640625

Combine like terms: 0.5 + 0.31640625 = 0.81640625
0.31640625 + 1.125x + x2 = 0.81640625

Factor a perfect square on the left side:
(x + 0.5625)(x + 0.5625) = 0.81640625

Calculate the square root of the right side: 0.903552018

Break this problem into two subproblems by setting 
(x + 0.5625) equal to 0.903552018 and -0.903552018.

Subproblem 1

x + 0.5625 = 0.903552018 Simplifying x + 0.5625 = 0.903552018 Reorder the terms: 0.5625 + x = 0.903552018 Solving 0.5625 + x = 0.903552018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 0.903552018 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 0.903552018 + -0.5625 x = 0.903552018 + -0.5625 Combine like terms: 0.903552018 + -0.5625 = 0.341052018 x = 0.341052018 Simplifying x = 0.341052018

Subproblem 2

x + 0.5625 = -0.903552018 Simplifying x + 0.5625 = -0.903552018 Reorder the terms: 0.5625 + x = -0.903552018 Solving 0.5625 + x = -0.903552018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -0.903552018 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -0.903552018 + -0.5625 x = -0.903552018 + -0.5625 Combine like terms: -0.903552018 + -0.5625 = -1.466052018 x = -1.466052018 Simplifying x = -1.466052018

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.341052018, -1.466052018}

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