0=0.5x^2-25x+96

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Solution for 0=0.5x^2-25x+96 equation:


Simplifying
0 = 0.5x2 + -25x + 96

Reorder the terms:
0 = 96 + -25x + 0.5x2

Solving
0 = 96 + -25x + 0.5x2

Solving for variable 'x'.

Combine like terms: 0 + -96 = -96
-96 + 25x + -0.5x2 = 96 + -25x + 0.5x2 + -96 + 25x + -0.5x2

Reorder the terms:
-96 + 25x + -0.5x2 = 96 + -96 + -25x + 25x + 0.5x2 + -0.5x2

Combine like terms: 96 + -96 = 0
-96 + 25x + -0.5x2 = 0 + -25x + 25x + 0.5x2 + -0.5x2
-96 + 25x + -0.5x2 = -25x + 25x + 0.5x2 + -0.5x2

Combine like terms: -25x + 25x = 0
-96 + 25x + -0.5x2 = 0 + 0.5x2 + -0.5x2
-96 + 25x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
-96 + 25x + -0.5x2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
192 + -50x + x2 = 0

Move the constant term to the right:

Add '-192' to each side of the equation.
192 + -50x + -192 + x2 = 0 + -192

Reorder the terms:
192 + -192 + -50x + x2 = 0 + -192

Combine like terms: 192 + -192 = 0
0 + -50x + x2 = 0 + -192
-50x + x2 = 0 + -192

Combine like terms: 0 + -192 = -192
-50x + x2 = -192

The x term is -50x.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50x + 625 + x2 = -192 + 625

Reorder the terms:
625 + -50x + x2 = -192 + 625

Combine like terms: -192 + 625 = 433
625 + -50x + x2 = 433

Factor a perfect square on the left side:
(x + -25)(x + -25) = 433

Calculate the square root of the right side: 20.808652047

Break this problem into two subproblems by setting 
(x + -25) equal to 20.808652047 and -20.808652047.

Subproblem 1

x + -25 = 20.808652047 Simplifying x + -25 = 20.808652047 Reorder the terms: -25 + x = 20.808652047 Solving -25 + x = 20.808652047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 20.808652047 + 25 Combine like terms: -25 + 25 = 0 0 + x = 20.808652047 + 25 x = 20.808652047 + 25 Combine like terms: 20.808652047 + 25 = 45.808652047 x = 45.808652047 Simplifying x = 45.808652047

Subproblem 2

x + -25 = -20.808652047 Simplifying x + -25 = -20.808652047 Reorder the terms: -25 + x = -20.808652047 Solving -25 + x = -20.808652047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -20.808652047 + 25 Combine like terms: -25 + 25 = 0 0 + x = -20.808652047 + 25 x = -20.808652047 + 25 Combine like terms: -20.808652047 + 25 = 4.191347953 x = 4.191347953 Simplifying x = 4.191347953

Solution

The solution to the problem is based on the solutions from the subproblems. x = {45.808652047, 4.191347953}

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