175=-0.5x^2+25x

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Solution for 175=-0.5x^2+25x equation:


Simplifying
175 = -0.5x2 + 25x

Reorder the terms:
175 = 25x + -0.5x2

Solving
175 = 25x + -0.5x2

Solving for variable 'x'.

Reorder the terms:
175 + -25x + 0.5x2 = 25x + -25x + -0.5x2 + 0.5x2

Combine like terms: 25x + -25x = 0
175 + -25x + 0.5x2 = 0 + -0.5x2 + 0.5x2
175 + -25x + 0.5x2 = -0.5x2 + 0.5x2

Combine like terms: -0.5x2 + 0.5x2 = 0.0
175 + -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'.
350 + -50x + x2 = 0

Move the constant term to the right:

Add '-350' to each side of the equation.
350 + -50x + -350 + x2 = 0 + -350

Reorder the terms:
350 + -350 + -50x + x2 = 0 + -350

Combine like terms: 350 + -350 = 0
0 + -50x + x2 = 0 + -350
-50x + x2 = 0 + -350

Combine like terms: 0 + -350 = -350
-50x + x2 = -350

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 = -350 + 625

Reorder the terms:
625 + -50x + x2 = -350 + 625

Combine like terms: -350 + 625 = 275
625 + -50x + x2 = 275

Factor a perfect square on the left side:
(x + -25)(x + -25) = 275

Calculate the square root of the right side: 16.583123952

Break this problem into two subproblems by setting 
(x + -25) equal to 16.583123952 and -16.583123952.

Subproblem 1

x + -25 = 16.583123952 Simplifying x + -25 = 16.583123952 Reorder the terms: -25 + x = 16.583123952 Solving -25 + x = 16.583123952 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 = 16.583123952 + 25 Combine like terms: -25 + 25 = 0 0 + x = 16.583123952 + 25 x = 16.583123952 + 25 Combine like terms: 16.583123952 + 25 = 41.583123952 x = 41.583123952 Simplifying x = 41.583123952

Subproblem 2

x + -25 = -16.583123952 Simplifying x + -25 = -16.583123952 Reorder the terms: -25 + x = -16.583123952 Solving -25 + x = -16.583123952 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 = -16.583123952 + 25 Combine like terms: -25 + 25 = 0 0 + x = -16.583123952 + 25 x = -16.583123952 + 25 Combine like terms: -16.583123952 + 25 = 8.416876048 x = 8.416876048 Simplifying x = 8.416876048

Solution

The solution to the problem is based on the solutions from the subproblems. x = {41.583123952, 8.416876048}

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