25x^2+30x-18=0

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Solution for 25x^2+30x-18=0 equation:


Simplifying
25x2 + 30x + -18 = 0

Reorder the terms:
-18 + 30x + 25x2 = 0

Solving
-18 + 30x + 25x2 = 0

Solving for variable 'x'.

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

Divide each side by '25'.
-0.72 + 1.2x + x2 = 0

Move the constant term to the right:

Add '0.72' to each side of the equation.
-0.72 + 1.2x + 0.72 + x2 = 0 + 0.72

Reorder the terms:
-0.72 + 0.72 + 1.2x + x2 = 0 + 0.72

Combine like terms: -0.72 + 0.72 = 0.00
0.00 + 1.2x + x2 = 0 + 0.72
1.2x + x2 = 0 + 0.72

Combine like terms: 0 + 0.72 = 0.72
1.2x + x2 = 0.72

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 = 0.72 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = 0.72 + 0.36

Combine like terms: 0.72 + 0.36 = 1.08
0.36 + 1.2x + x2 = 1.08

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = 1.08

Calculate the square root of the right side: 1.039230485

Break this problem into two subproblems by setting 
(x + 0.6) equal to 1.039230485 and -1.039230485.

Subproblem 1

x + 0.6 = 1.039230485 Simplifying x + 0.6 = 1.039230485 Reorder the terms: 0.6 + x = 1.039230485 Solving 0.6 + x = 1.039230485 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 = 1.039230485 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 1.039230485 + -0.6 x = 1.039230485 + -0.6 Combine like terms: 1.039230485 + -0.6 = 0.439230485 x = 0.439230485 Simplifying x = 0.439230485

Subproblem 2

x + 0.6 = -1.039230485 Simplifying x + 0.6 = -1.039230485 Reorder the terms: 0.6 + x = -1.039230485 Solving 0.6 + x = -1.039230485 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 = -1.039230485 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -1.039230485 + -0.6 x = -1.039230485 + -0.6 Combine like terms: -1.039230485 + -0.6 = -1.639230485 x = -1.639230485 Simplifying x = -1.639230485

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.439230485, -1.639230485}

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