4x^2-27x-576=0

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Solution for 4x^2-27x-576=0 equation:


Simplifying
4x2 + -27x + -576 = 0

Reorder the terms:
-576 + -27x + 4x2 = 0

Solving
-576 + -27x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-144 + -6.75x + x2 = 0

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + -6.75x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + -6.75x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + -6.75x + x2 = 0 + 144
-6.75x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
-6.75x + x2 = 144

The x term is -6.75x.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75x + 11.390625 + x2 = 144 + 11.390625

Reorder the terms:
11.390625 + -6.75x + x2 = 144 + 11.390625

Combine like terms: 144 + 11.390625 = 155.390625
11.390625 + -6.75x + x2 = 155.390625

Factor a perfect square on the left side:
(x + -3.375)(x + -3.375) = 155.390625

Calculate the square root of the right side: 12.465577604

Break this problem into two subproblems by setting 
(x + -3.375) equal to 12.465577604 and -12.465577604.

Subproblem 1

x + -3.375 = 12.465577604 Simplifying x + -3.375 = 12.465577604 Reorder the terms: -3.375 + x = 12.465577604 Solving -3.375 + x = 12.465577604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 12.465577604 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 12.465577604 + 3.375 x = 12.465577604 + 3.375 Combine like terms: 12.465577604 + 3.375 = 15.840577604 x = 15.840577604 Simplifying x = 15.840577604

Subproblem 2

x + -3.375 = -12.465577604 Simplifying x + -3.375 = -12.465577604 Reorder the terms: -3.375 + x = -12.465577604 Solving -3.375 + x = -12.465577604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -12.465577604 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -12.465577604 + 3.375 x = -12.465577604 + 3.375 Combine like terms: -12.465577604 + 3.375 = -9.090577604 x = -9.090577604 Simplifying x = -9.090577604

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.840577604, -9.090577604}

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