30x^2+24x-25=0

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Solution for 30x^2+24x-25=0 equation: 


Simplifying
30x2 + 24x + -25 = 0

Reorder the terms:
-25 + 24x + 30x2 = 0

Solving
-25 + 24x + 30x2 = 0

Solving for variable 'x'.

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

Divide each side by '30'.
-0.8333333333 + 0.8x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + 0.8x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + 0.8x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + 0.8x + x2 = 0 + 0.8333333333
0.8x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
0.8x + x2 = 0.8333333333

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 0.8333333333 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 0.8333333333 + 0.16

Combine like terms: 0.8333333333 + 0.16 = 0.9933333333
0.16 + 0.8x + x2 = 0.9933333333

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 0.9933333333

Calculate the square root of the right side: 0.996661092

Break this problem into two subproblems by setting 
(x + 0.4) equal to 0.996661092 and -0.996661092.


Subproblem 1
x + 0.4 = 0.996661092

Simplifying
x + 0.4 = 0.996661092

Reorder the terms:
0.4 + x = 0.996661092

Solving
0.4 + x = 0.996661092

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 0.996661092 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 0.996661092 + -0.4
x = 0.996661092 + -0.4

Combine like terms: 0.996661092 + -0.4 = 0.596661092
x = 0.596661092

Simplifying
x = 0.596661092


Subproblem 2
x + 0.4 = -0.996661092

Simplifying
x + 0.4 = -0.996661092

Reorder the terms:
0.4 + x = -0.996661092

Solving
0.4 + x = -0.996661092

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -0.996661092 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -0.996661092 + -0.4
x = -0.996661092 + -0.4

Combine like terms: -0.996661092 + -0.4 = -1.396661092
x = -1.396661092

Simplifying
x = -1.396661092


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.596661092, -1.396661092}

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