25x^2+30x=12

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Solution for 25x^2+30x=12 equation:


Simplifying
25x2 + 30x = 12

Reorder the terms:
30x + 25x2 = 12

Solving
30x + 25x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 30x + 25x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 30x + 25x2 = 0

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

Divide each side by '25'.
-0.48 + 1.2x + x2 = 0

Move the constant term to the right:

Add '0.48' to each side of the equation.
-0.48 + 1.2x + 0.48 + x2 = 0 + 0.48

Reorder the terms:
-0.48 + 0.48 + 1.2x + x2 = 0 + 0.48

Combine like terms: -0.48 + 0.48 = 0.00
0.00 + 1.2x + x2 = 0 + 0.48
1.2x + x2 = 0 + 0.48

Combine like terms: 0 + 0.48 = 0.48
1.2x + x2 = 0.48

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 = 0.48 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = 0.48 + 0.36

Combine like terms: 0.48 + 0.36 = 0.84
0.36 + 1.2x + x2 = 0.84

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = 0.84

Calculate the square root of the right side: 0.916515139

Break this problem into two subproblems by setting 
(x + 0.6) equal to 0.916515139 and -0.916515139.

Subproblem 1

x + 0.6 = 0.916515139 Simplifying x + 0.6 = 0.916515139 Reorder the terms: 0.6 + x = 0.916515139 Solving 0.6 + x = 0.916515139 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 = 0.916515139 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.916515139 + -0.6 x = 0.916515139 + -0.6 Combine like terms: 0.916515139 + -0.6 = 0.316515139 x = 0.316515139 Simplifying x = 0.316515139

Subproblem 2

x + 0.6 = -0.916515139 Simplifying x + 0.6 = -0.916515139 Reorder the terms: 0.6 + x = -0.916515139 Solving 0.6 + x = -0.916515139 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 = -0.916515139 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.916515139 + -0.6 x = -0.916515139 + -0.6 Combine like terms: -0.916515139 + -0.6 = -1.516515139 x = -1.516515139 Simplifying x = -1.516515139

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.316515139, -1.516515139}

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