25x^2+60x=39

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Solution for 25x^2+60x=39 equation:


Simplifying
25x2 + 60x = 39

Reorder the terms:
60x + 25x2 = 39

Solving
60x + 25x2 = 39

Solving for variable 'x'.

Reorder the terms:
-39 + 60x + 25x2 = 39 + -39

Combine like terms: 39 + -39 = 0
-39 + 60x + 25x2 = 0

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

Divide each side by '25'.
-1.56 + 2.4x + x2 = 0

Move the constant term to the right:

Add '1.56' to each side of the equation.
-1.56 + 2.4x + 1.56 + x2 = 0 + 1.56

Reorder the terms:
-1.56 + 1.56 + 2.4x + x2 = 0 + 1.56

Combine like terms: -1.56 + 1.56 = 0.00
0.00 + 2.4x + x2 = 0 + 1.56
2.4x + x2 = 0 + 1.56

Combine like terms: 0 + 1.56 = 1.56
2.4x + x2 = 1.56

The x term is 2.4x.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4x + 1.44 + x2 = 1.56 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = 1.56 + 1.44

Combine like terms: 1.56 + 1.44 = 3
1.44 + 2.4x + x2 = 3

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 1.2) equal to 1.732050808 and -1.732050808.

Subproblem 1

x + 1.2 = 1.732050808 Simplifying x + 1.2 = 1.732050808 Reorder the terms: 1.2 + x = 1.732050808 Solving 1.2 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 1.732050808 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.732050808 + -1.2 x = 1.732050808 + -1.2 Combine like terms: 1.732050808 + -1.2 = 0.532050808 x = 0.532050808 Simplifying x = 0.532050808

Subproblem 2

x + 1.2 = -1.732050808 Simplifying x + 1.2 = -1.732050808 Reorder the terms: 1.2 + x = -1.732050808 Solving 1.2 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -1.732050808 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.732050808 + -1.2 x = -1.732050808 + -1.2 Combine like terms: -1.732050808 + -1.2 = -2.932050808 x = -2.932050808 Simplifying x = -2.932050808

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.532050808, -2.932050808}

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