4x(8x-18)=-30

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Solution for 4x(8x-18)=-30 equation: 


Simplifying
4x(8x + -18) = -30

Reorder the terms:
4x(-18 + 8x) = -30
(-18 * 4x + 8x * 4x) = -30
(-72x + 32x2) = -30

Solving
-72x + 32x2 = -30

Solving for variable 'x'.

Reorder the terms:
30 + -72x + 32x2 = -30 + 30

Combine like terms: -30 + 30 = 0
30 + -72x + 32x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -36x + 16x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + -36x + 16x2)' equal to zero and attempt to solve:

Simplifying
15 + -36x + 16x2 = 0

Solving
15 + -36x + 16x2 = 0

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

Divide each side by '16'.
0.9375 + -2.25x + x2 = 0

Move the constant term to the right:

Add '-0.9375' to each side of the equation.
0.9375 + -2.25x + -0.9375 + x2 = 0 + -0.9375

Reorder the terms:
0.9375 + -0.9375 + -2.25x + x2 = 0 + -0.9375

Combine like terms: 0.9375 + -0.9375 = 0.0000
0.0000 + -2.25x + x2 = 0 + -0.9375
-2.25x + x2 = 0 + -0.9375

Combine like terms: 0 + -0.9375 = -0.9375
-2.25x + x2 = -0.9375

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = -0.9375 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = -0.9375 + 1.265625

Combine like terms: -0.9375 + 1.265625 = 0.328125
1.265625 + -2.25x + x2 = 0.328125

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 0.328125

Calculate the square root of the right side: 0.572821962

Break this problem into two subproblems by setting 
(x + -1.125) equal to 0.572821962 and -0.572821962.


Subproblem 1
x + -1.125 = 0.572821962

Simplifying
x + -1.125 = 0.572821962

Reorder the terms:
-1.125 + x = 0.572821962

Solving
-1.125 + x = 0.572821962

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 0.572821962 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 0.572821962 + 1.125
x = 0.572821962 + 1.125

Combine like terms: 0.572821962 + 1.125 = 1.697821962
x = 1.697821962

Simplifying
x = 1.697821962


Subproblem 2
x + -1.125 = -0.572821962

Simplifying
x + -1.125 = -0.572821962

Reorder the terms:
-1.125 + x = -0.572821962

Solving
-1.125 + x = -0.572821962

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -0.572821962 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -0.572821962 + 1.125
x = -0.572821962 + 1.125

Combine like terms: -0.572821962 + 1.125 = 0.552178038
x = 0.552178038

Simplifying
x = 0.552178038


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.697821962, 0.552178038}
Solution
x = {1.697821962, 0.552178038}

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