A^2-30A+112.5=0

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Solution for A^2-30A+112.5=0 equation:


Simplifying
A2 + -30A + 112.5 = 0

Reorder the terms:
112.5 + -30A + A2 = 0

Solving
112.5 + -30A + A2 = 0

Solving for variable 'A'.

Begin completing the square.

Move the constant term to the right:

Add '-112.5' to each side of the equation.
112.5 + -30A + -112.5 + A2 = 0 + -112.5

Reorder the terms:
112.5 + -112.5 + -30A + A2 = 0 + -112.5

Combine like terms: 112.5 + -112.5 = 0.0
0.0 + -30A + A2 = 0 + -112.5
-30A + A2 = 0 + -112.5

Combine like terms: 0 + -112.5 = -112.5
-30A + A2 = -112.5

The A term is -30A.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30A + 225 + A2 = -112.5 + 225

Reorder the terms:
225 + -30A + A2 = -112.5 + 225

Combine like terms: -112.5 + 225 = 112.5
225 + -30A + A2 = 112.5

Factor a perfect square on the left side:
(A + -15)(A + -15) = 112.5

Calculate the square root of the right side: 10.606601718

Break this problem into two subproblems by setting 
(A + -15) equal to 10.606601718 and -10.606601718.

Subproblem 1

A + -15 = 10.606601718 Simplifying A + -15 = 10.606601718 Reorder the terms: -15 + A = 10.606601718 Solving -15 + A = 10.606601718 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + A = 10.606601718 + 15 Combine like terms: -15 + 15 = 0 0 + A = 10.606601718 + 15 A = 10.606601718 + 15 Combine like terms: 10.606601718 + 15 = 25.606601718 A = 25.606601718 Simplifying A = 25.606601718

Subproblem 2

A + -15 = -10.606601718 Simplifying A + -15 = -10.606601718 Reorder the terms: -15 + A = -10.606601718 Solving -15 + A = -10.606601718 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + A = -10.606601718 + 15 Combine like terms: -15 + 15 = 0 0 + A = -10.606601718 + 15 A = -10.606601718 + 15 Combine like terms: -10.606601718 + 15 = 4.393398282 A = 4.393398282 Simplifying A = 4.393398282

Solution

The solution to the problem is based on the solutions from the subproblems. A = {25.606601718, 4.393398282}

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