4x^2+9x-6=0

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Solution for 4x^2+9x-6=0 equation:


Simplifying
4x2 + 9x + -6 = 0

Reorder the terms:
-6 + 9x + 4x2 = 0

Solving
-6 + 9x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-1.5 + 2.25x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 2.25x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 2.25x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 2.25x + x2 = 0 + 1.5
2.25x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
2.25x + x2 = 1.5

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 = 1.5 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 1.5 + 1.265625

Combine like terms: 1.5 + 1.265625 = 2.765625
1.265625 + 2.25x + x2 = 2.765625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 2.765625

Calculate the square root of the right side: 1.663016837

Break this problem into two subproblems by setting 
(x + 1.125) equal to 1.663016837 and -1.663016837.

Subproblem 1

x + 1.125 = 1.663016837 Simplifying x + 1.125 = 1.663016837 Reorder the terms: 1.125 + x = 1.663016837 Solving 1.125 + x = 1.663016837 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 = 1.663016837 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 1.663016837 + -1.125 x = 1.663016837 + -1.125 Combine like terms: 1.663016837 + -1.125 = 0.538016837 x = 0.538016837 Simplifying x = 0.538016837

Subproblem 2

x + 1.125 = -1.663016837 Simplifying x + 1.125 = -1.663016837 Reorder the terms: 1.125 + x = -1.663016837 Solving 1.125 + x = -1.663016837 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 = -1.663016837 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -1.663016837 + -1.125 x = -1.663016837 + -1.125 Combine like terms: -1.663016837 + -1.125 = -2.788016837 x = -2.788016837 Simplifying x = -2.788016837

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.538016837, -2.788016837}

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