0=-2x^2+8x+5

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Solution for 0=-2x^2+8x+5 equation:


Simplifying
0 = -2x2 + 8x + 5

Reorder the terms:
0 = 5 + 8x + -2x2

Solving
0 = 5 + 8x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -8x + 2x2 = 5 + 8x + -2x2 + -5 + -8x + 2x2

Reorder the terms:
-5 + -8x + 2x2 = 5 + -5 + 8x + -8x + -2x2 + 2x2

Combine like terms: 5 + -5 = 0
-5 + -8x + 2x2 = 0 + 8x + -8x + -2x2 + 2x2
-5 + -8x + 2x2 = 8x + -8x + -2x2 + 2x2

Combine like terms: 8x + -8x = 0
-5 + -8x + 2x2 = 0 + -2x2 + 2x2
-5 + -8x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-5 + -8x + 2x2 = 0

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

Divide each side by '2'.
-2.5 + -4x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -4x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -4x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -4x + x2 = 0 + 2.5
-4x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-4x + x2 = 2.5

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 2.5 + 4

Reorder the terms:
4 + -4x + x2 = 2.5 + 4

Combine like terms: 2.5 + 4 = 6.5
4 + -4x + x2 = 6.5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 6.5

Calculate the square root of the right side: 2.549509757

Break this problem into two subproblems by setting 
(x + -2) equal to 2.549509757 and -2.549509757.

Subproblem 1

x + -2 = 2.549509757 Simplifying x + -2 = 2.549509757 Reorder the terms: -2 + x = 2.549509757 Solving -2 + x = 2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.549509757 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.549509757 + 2 x = 2.549509757 + 2 Combine like terms: 2.549509757 + 2 = 4.549509757 x = 4.549509757 Simplifying x = 4.549509757

Subproblem 2

x + -2 = -2.549509757 Simplifying x + -2 = -2.549509757 Reorder the terms: -2 + x = -2.549509757 Solving -2 + x = -2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.549509757 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.549509757 + 2 x = -2.549509757 + 2 Combine like terms: -2.549509757 + 2 = -0.549509757 x = -0.549509757 Simplifying x = -0.549509757

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.549509757, -0.549509757}

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