75x-x^2=1406.25

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Solution for 75x-x^2=1406.25 equation:


Simplifying
75x + -1x2 = 1406.25

Solving
75x + -1x2 = 1406.25

Solving for variable 'x'.

Reorder the terms:
-1406.25 + 75x + -1x2 = 1406.25 + -1406.25

Combine like terms: 1406.25 + -1406.25 = 0.00
-1406.25 + 75x + -1x2 = 0.00

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

Divide each side by '-1'.
1406.25 + -75x + x2 = 0.00

Move the constant term to the right:

Add '-1406.25' to each side of the equation.
1406.25 + -75x + -1406.25 + x2 = 0.00 + -1406.25

Reorder the terms:
1406.25 + -1406.25 + -75x + x2 = 0.00 + -1406.25

Combine like terms: 1406.25 + -1406.25 = 0.00
0.00 + -75x + x2 = 0.00 + -1406.25
-75x + x2 = 0.00 + -1406.25

Combine like terms: 0.00 + -1406.25 = -1406.25
-75x + x2 = -1406.25

The x term is -75x.  Take half its coefficient (-37.5).
Square it (1406.25) and add it to both sides.

Add '1406.25' to each side of the equation.
-75x + 1406.25 + x2 = -1406.25 + 1406.25

Reorder the terms:
1406.25 + -75x + x2 = -1406.25 + 1406.25

Combine like terms: -1406.25 + 1406.25 = 0.00
1406.25 + -75x + x2 = 0.00

Factor a perfect square on the left side:
(x + -37.5)(x + -37.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + -37.5) equal to 0.00 and 0.00.

Subproblem 1

x + -37.5 = 0.00 Simplifying x + -37.5 = 0.00 Reorder the terms: -37.5 + x = 0.00 Solving -37.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = 0.00 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = 0.00 + 37.5 x = 0.00 + 37.5 Combine like terms: 0.00 + 37.5 = 37.5 x = 37.5 Simplifying x = 37.5

Subproblem 2

x + -37.5 = 0.00 Simplifying x + -37.5 = 0.00 Reorder the terms: -37.5 + x = 0.00 Solving -37.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = 0.00 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = 0.00 + 37.5 x = 0.00 + 37.5 Combine like terms: 0.00 + 37.5 = 37.5 x = 37.5 Simplifying x = 37.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {37.5, 37.5}

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