5x-0.25x^2-17=0

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Solution for 5x-0.25x^2-17=0 equation:


Simplifying
5x + -0.25x2 + -17 = 0

Reorder the terms:
-17 + 5x + -0.25x2 = 0

Solving
-17 + 5x + -0.25x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.25 the coefficient of the squared term: 

Divide each side by '-0.25'.
68 + -20x + x2 = 0

Move the constant term to the right:

Add '-68' to each side of the equation.
68 + -20x + -68 + x2 = 0 + -68

Reorder the terms:
68 + -68 + -20x + x2 = 0 + -68

Combine like terms: 68 + -68 = 0
0 + -20x + x2 = 0 + -68
-20x + x2 = 0 + -68

Combine like terms: 0 + -68 = -68
-20x + x2 = -68

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -68 + 100

Reorder the terms:
100 + -20x + x2 = -68 + 100

Combine like terms: -68 + 100 = 32
100 + -20x + x2 = 32

Factor a perfect square on the left side:
(x + -10)(x + -10) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + -10) equal to 5.656854249 and -5.656854249.

Subproblem 1

x + -10 = 5.656854249 Simplifying x + -10 = 5.656854249 Reorder the terms: -10 + x = 5.656854249 Solving -10 + x = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 5.656854249 + 10 Combine like terms: -10 + 10 = 0 0 + x = 5.656854249 + 10 x = 5.656854249 + 10 Combine like terms: 5.656854249 + 10 = 15.656854249 x = 15.656854249 Simplifying x = 15.656854249

Subproblem 2

x + -10 = -5.656854249 Simplifying x + -10 = -5.656854249 Reorder the terms: -10 + x = -5.656854249 Solving -10 + x = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -5.656854249 + 10 Combine like terms: -10 + 10 = 0 0 + x = -5.656854249 + 10 x = -5.656854249 + 10 Combine like terms: -5.656854249 + 10 = 4.343145751 x = 4.343145751 Simplifying x = 4.343145751

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.656854249, 4.343145751}

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