25X^2-30X+9=125

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Solution for 25X^2-30X+9=125 equation:


Simplifying
25X2 + -30X + 9 = 125

Reorder the terms:
9 + -30X + 25X2 = 125

Solving
9 + -30X + 25X2 = 125

Solving for variable 'X'.

Reorder the terms:
9 + -125 + -30X + 25X2 = 125 + -125

Combine like terms: 9 + -125 = -116
-116 + -30X + 25X2 = 125 + -125

Combine like terms: 125 + -125 = 0
-116 + -30X + 25X2 = 0

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

Divide each side by '25'.
-4.64 + -1.2X + X2 = 0

Move the constant term to the right:

Add '4.64' to each side of the equation.
-4.64 + -1.2X + 4.64 + X2 = 0 + 4.64

Reorder the terms:
-4.64 + 4.64 + -1.2X + X2 = 0 + 4.64

Combine like terms: -4.64 + 4.64 = 0.00
0.00 + -1.2X + X2 = 0 + 4.64
-1.2X + X2 = 0 + 4.64

Combine like terms: 0 + 4.64 = 4.64
-1.2X + X2 = 4.64

The X term is -1.2X.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2X + 0.36 + X2 = 4.64 + 0.36

Reorder the terms:
0.36 + -1.2X + X2 = 4.64 + 0.36

Combine like terms: 4.64 + 0.36 = 5
0.36 + -1.2X + X2 = 5

Factor a perfect square on the left side:
(X + -0.6)(X + -0.6) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(X + -0.6) equal to 2.236067978 and -2.236067978.

Subproblem 1

X + -0.6 = 2.236067978 Simplifying X + -0.6 = 2.236067978 Reorder the terms: -0.6 + X = 2.236067978 Solving -0.6 + X = 2.236067978 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + X = 2.236067978 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + X = 2.236067978 + 0.6 X = 2.236067978 + 0.6 Combine like terms: 2.236067978 + 0.6 = 2.836067978 X = 2.836067978 Simplifying X = 2.836067978

Subproblem 2

X + -0.6 = -2.236067978 Simplifying X + -0.6 = -2.236067978 Reorder the terms: -0.6 + X = -2.236067978 Solving -0.6 + X = -2.236067978 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + X = -2.236067978 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + X = -2.236067978 + 0.6 X = -2.236067978 + 0.6 Combine like terms: -2.236067978 + 0.6 = -1.636067978 X = -1.636067978 Simplifying X = -1.636067978

Solution

The solution to the problem is based on the solutions from the subproblems. X = {2.836067978, -1.636067978}

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