-2x^2+16x+9=0

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Solution for -2x^2+16x+9=0 equation:


Simplifying
-2x2 + 16x + 9 = 0

Reorder the terms:
9 + 16x + -2x2 = 0

Solving
9 + 16x + -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'.
-4.5 + -8x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -8x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -8x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -8x + x2 = 0 + 4.5
-8x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-8x + x2 = 4.5

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 4.5 + 16

Reorder the terms:
16 + -8x + x2 = 4.5 + 16

Combine like terms: 4.5 + 16 = 20.5
16 + -8x + x2 = 20.5

Factor a perfect square on the left side:
(x + -4)(x + -4) = 20.5

Calculate the square root of the right side: 4.527692569

Break this problem into two subproblems by setting 
(x + -4) equal to 4.527692569 and -4.527692569.

Subproblem 1

x + -4 = 4.527692569 Simplifying x + -4 = 4.527692569 Reorder the terms: -4 + x = 4.527692569 Solving -4 + x = 4.527692569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.527692569 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.527692569 + 4 x = 4.527692569 + 4 Combine like terms: 4.527692569 + 4 = 8.527692569 x = 8.527692569 Simplifying x = 8.527692569

Subproblem 2

x + -4 = -4.527692569 Simplifying x + -4 = -4.527692569 Reorder the terms: -4 + x = -4.527692569 Solving -4 + x = -4.527692569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.527692569 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.527692569 + 4 x = -4.527692569 + 4 Combine like terms: -4.527692569 + 4 = -0.527692569 x = -0.527692569 Simplifying x = -0.527692569

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.527692569, -0.527692569}

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