4x^2+30x-300=

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Solution for 4x^2+30x-300= equation: 


Simplifying
4x2 + 30x + -300 = 0

Reorder the terms:
-300 + 30x + 4x2 = 0

Solving
-300 + 30x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-150 + 15x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-150 + 15x + 2x2)' equal to zero and attempt to solve:

Simplifying
-150 + 15x + 2x2 = 0

Solving
-150 + 15x + 2x2 = 0

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

Divide each side by '2'.
-75 + 7.5x + x2 = 0

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 7.5x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + 7.5x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 7.5x + x2 = 0 + 75
7.5x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
7.5x + x2 = 75

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = 75 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 75 + 14.0625

Combine like terms: 75 + 14.0625 = 89.0625
14.0625 + 7.5x + x2 = 89.0625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 89.0625

Calculate the square root of the right side: 9.437293044

Break this problem into two subproblems by setting 
(x + 3.75) equal to 9.437293044 and -9.437293044.


Subproblem 1
x + 3.75 = 9.437293044

Simplifying
x + 3.75 = 9.437293044

Reorder the terms:
3.75 + x = 9.437293044

Solving
3.75 + x = 9.437293044

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = 9.437293044 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 9.437293044 + -3.75
x = 9.437293044 + -3.75

Combine like terms: 9.437293044 + -3.75 = 5.687293044
x = 5.687293044

Simplifying
x = 5.687293044


Subproblem 2
x + 3.75 = -9.437293044

Simplifying
x + 3.75 = -9.437293044

Reorder the terms:
3.75 + x = -9.437293044

Solving
3.75 + x = -9.437293044

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = -9.437293044 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -9.437293044 + -3.75
x = -9.437293044 + -3.75

Combine like terms: -9.437293044 + -3.75 = -13.187293044
x = -13.187293044

Simplifying
x = -13.187293044


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.687293044, -13.187293044}
Solution
x = {5.687293044, -13.187293044}

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