-2x^2-9x+4=0

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


Simplifying
-2x2 + -9x + 4 = 0

Reorder the terms:
4 + -9x + -2x2 = 0

Solving
4 + -9x + -2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-2 + 4.5x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4.5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 4.5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 4.5x + x2 = 0 + 2
4.5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
4.5x + x2 = 2

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 2 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 2 + 5.0625

Combine like terms: 2 + 5.0625 = 7.0625
5.0625 + 4.5x + x2 = 7.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.657536453 and -2.657536453.

Subproblem 1

x + 2.25 = 2.657536453 Simplifying x + 2.25 = 2.657536453 Reorder the terms: 2.25 + x = 2.657536453 Solving 2.25 + x = 2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 2.657536453 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.657536453 + -2.25 x = 2.657536453 + -2.25 Combine like terms: 2.657536453 + -2.25 = 0.407536453 x = 0.407536453 Simplifying x = 0.407536453

Subproblem 2

x + 2.25 = -2.657536453 Simplifying x + 2.25 = -2.657536453 Reorder the terms: 2.25 + x = -2.657536453 Solving 2.25 + x = -2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -2.657536453 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.657536453 + -2.25 x = -2.657536453 + -2.25 Combine like terms: -2.657536453 + -2.25 = -4.907536453 x = -4.907536453 Simplifying x = -4.907536453

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.407536453, -4.907536453}

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