52.5-24x+1.2x^2=0

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Solution for 52.5-24x+1.2x^2=0 equation:


Simplifying
52.5 + -24x + 1.2x2 = 0

Solving
52.5 + -24x + 1.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.2'.
43.75 + -20x + x2 = 0

Move the constant term to the right:

Add '-43.75' to each side of the equation.
43.75 + -20x + -43.75 + x2 = 0 + -43.75

Reorder the terms:
43.75 + -43.75 + -20x + x2 = 0 + -43.75

Combine like terms: 43.75 + -43.75 = 0.00
0.00 + -20x + x2 = 0 + -43.75
-20x + x2 = 0 + -43.75

Combine like terms: 0 + -43.75 = -43.75
-20x + x2 = -43.75

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 = -43.75 + 100

Reorder the terms:
100 + -20x + x2 = -43.75 + 100

Combine like terms: -43.75 + 100 = 56.25
100 + -20x + x2 = 56.25

Factor a perfect square on the left side:
(x + -10)(x + -10) = 56.25

Calculate the square root of the right side: 7.5

Break this problem into two subproblems by setting 
(x + -10) equal to 7.5 and -7.5.

Subproblem 1

x + -10 = 7.5 Simplifying x + -10 = 7.5 Reorder the terms: -10 + x = 7.5 Solving -10 + x = 7.5 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 = 7.5 + 10 Combine like terms: -10 + 10 = 0 0 + x = 7.5 + 10 x = 7.5 + 10 Combine like terms: 7.5 + 10 = 17.5 x = 17.5 Simplifying x = 17.5

Subproblem 2

x + -10 = -7.5 Simplifying x + -10 = -7.5 Reorder the terms: -10 + x = -7.5 Solving -10 + x = -7.5 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 = -7.5 + 10 Combine like terms: -10 + 10 = 0 0 + x = -7.5 + 10 x = -7.5 + 10 Combine like terms: -7.5 + 10 = 2.5 x = 2.5 Simplifying x = 2.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.5, 2.5}

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