-4x^2+8x+9=0

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


Simplifying
-4x2 + 8x + 9 = 0

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

Solving
9 + 8x + -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'.
-2.25 + -2x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -2x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -2x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -2x + x2 = 0 + 2.25
-2x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-2x + x2 = 2.25

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 2.25 + 1

Reorder the terms:
1 + -2x + x2 = 2.25 + 1

Combine like terms: 2.25 + 1 = 3.25
1 + -2x + x2 = 3.25

Factor a perfect square on the left side:
(x + -1)(x + -1) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -1) equal to 1.802775638 and -1.802775638.

Subproblem 1

x + -1 = 1.802775638 Simplifying x + -1 = 1.802775638 Reorder the terms: -1 + x = 1.802775638 Solving -1 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.802775638 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.802775638 + 1 x = 1.802775638 + 1 Combine like terms: 1.802775638 + 1 = 2.802775638 x = 2.802775638 Simplifying x = 2.802775638

Subproblem 2

x + -1 = -1.802775638 Simplifying x + -1 = -1.802775638 Reorder the terms: -1 + x = -1.802775638 Solving -1 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.802775638 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.802775638 + 1 x = -1.802775638 + 1 Combine like terms: -1.802775638 + 1 = -0.802775638 x = -0.802775638 Simplifying x = -0.802775638

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.802775638, -0.802775638}

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