-x^2+8.5x+4=0

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Solution for -x^2+8.5x+4=0 equation:


Simplifying
-1x2 + 8.5x + 4 = 0

Reorder the terms:
4 + 8.5x + -1x2 = 0

Solving
4 + 8.5x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + -8.5x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -8.5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -8.5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -8.5x + x2 = 0 + 4
-8.5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-8.5x + x2 = 4

The x term is -8.5x.  Take half its coefficient (-4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
-8.5x + 18.0625 + x2 = 4 + 18.0625

Reorder the terms:
18.0625 + -8.5x + x2 = 4 + 18.0625

Combine like terms: 4 + 18.0625 = 22.0625
18.0625 + -8.5x + x2 = 22.0625

Factor a perfect square on the left side:
(x + -4.25)(x + -4.25) = 22.0625

Calculate the square root of the right side: 4.697073557

Break this problem into two subproblems by setting 
(x + -4.25) equal to 4.697073557 and -4.697073557.

Subproblem 1

x + -4.25 = 4.697073557 Simplifying x + -4.25 = 4.697073557 Reorder the terms: -4.25 + x = 4.697073557 Solving -4.25 + x = 4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 4.697073557 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 4.697073557 + 4.25 x = 4.697073557 + 4.25 Combine like terms: 4.697073557 + 4.25 = 8.947073557 x = 8.947073557 Simplifying x = 8.947073557

Subproblem 2

x + -4.25 = -4.697073557 Simplifying x + -4.25 = -4.697073557 Reorder the terms: -4.25 + x = -4.697073557 Solving -4.25 + x = -4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -4.697073557 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -4.697073557 + 4.25 x = -4.697073557 + 4.25 Combine like terms: -4.697073557 + 4.25 = -0.447073557 x = -0.447073557 Simplifying x = -0.447073557

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.947073557, -0.447073557}

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