300=-0.02x^2+24x

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Solution for 300=-0.02x^2+24x equation:


Simplifying
300 = -0.02x2 + 24x

Reorder the terms:
300 = 24x + -0.02x2

Solving
300 = 24x + -0.02x2

Solving for variable 'x'.

Reorder the terms:
300 + -24x + 0.02x2 = 24x + -24x + -0.02x2 + 0.02x2

Combine like terms: 24x + -24x = 0
300 + -24x + 0.02x2 = 0 + -0.02x2 + 0.02x2
300 + -24x + 0.02x2 = -0.02x2 + 0.02x2

Combine like terms: -0.02x2 + 0.02x2 = 0.00
300 + -24x + 0.02x2 = 0.00

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

Divide each side by '0.02'.
15000 + -1200x + x2 = 0

Move the constant term to the right:

Add '-15000' to each side of the equation.
15000 + -1200x + -15000 + x2 = 0 + -15000

Reorder the terms:
15000 + -15000 + -1200x + x2 = 0 + -15000

Combine like terms: 15000 + -15000 = 0
0 + -1200x + x2 = 0 + -15000
-1200x + x2 = 0 + -15000

Combine like terms: 0 + -15000 = -15000
-1200x + x2 = -15000

The x term is -1200x.  Take half its coefficient (-600).
Square it (360000) and add it to both sides.

Add '360000' to each side of the equation.
-1200x + 360000 + x2 = -15000 + 360000

Reorder the terms:
360000 + -1200x + x2 = -15000 + 360000

Combine like terms: -15000 + 360000 = 345000
360000 + -1200x + x2 = 345000

Factor a perfect square on the left side:
(x + -600)(x + -600) = 345000

Calculate the square root of the right side: 587.367006224

Break this problem into two subproblems by setting 
(x + -600) equal to 587.367006224 and -587.367006224.


Subproblem 1
x + -600 = 587.367006224

Simplifying
x + -600 = 587.367006224

Reorder the terms:
-600 + x = 587.367006224

Solving
-600 + x = 587.367006224

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '600' to each side of the equation.
-600 + 600 + x = 587.367006224 + 600

Combine like terms: -600 + 600 = 0
0 + x = 587.367006224 + 600
x = 587.367006224 + 600

Combine like terms: 587.367006224 + 600 = 1187.367006224
x = 1187.367006224

Simplifying
x = 1187.367006224


Subproblem 2
x + -600 = -587.367006224

Simplifying
x + -600 = -587.367006224

Reorder the terms:
-600 + x = -587.367006224

Solving
-600 + x = -587.367006224

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '600' to each side of the equation.
-600 + 600 + x = -587.367006224 + 600

Combine like terms: -600 + 600 = 0
0 + x = -587.367006224 + 600
x = -587.367006224 + 600

Combine like terms: -587.367006224 + 600 = 12.632993776
x = 12.632993776

Simplifying
x = 12.632993776


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1187.367006224, 12.632993776}

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