3x^2+24x-53=0

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Solution for 3x^2+24x-53=0 equation:


Simplifying
3x2 + 24x + -53 = 0

Reorder the terms:
-53 + 24x + 3x2 = 0

Solving
-53 + 24x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-17.66666667 + 8x + x2 = 0

Move the constant term to the right:

Add '17.66666667' to each side of the equation.
-17.66666667 + 8x + 17.66666667 + x2 = 0 + 17.66666667

Reorder the terms:
-17.66666667 + 17.66666667 + 8x + x2 = 0 + 17.66666667

Combine like terms: -17.66666667 + 17.66666667 = 0.00000000
0.00000000 + 8x + x2 = 0 + 17.66666667
8x + x2 = 0 + 17.66666667

Combine like terms: 0 + 17.66666667 = 17.66666667
8x + x2 = 17.66666667

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 17.66666667 + 16

Reorder the terms:
16 + 8x + x2 = 17.66666667 + 16

Combine like terms: 17.66666667 + 16 = 33.66666667
16 + 8x + x2 = 33.66666667

Factor a perfect square on the left side:
(x + 4)(x + 4) = 33.66666667

Calculate the square root of the right side: 5.802298395

Break this problem into two subproblems by setting 
(x + 4) equal to 5.802298395 and -5.802298395.

Subproblem 1

x + 4 = 5.802298395 Simplifying x + 4 = 5.802298395 Reorder the terms: 4 + x = 5.802298395 Solving 4 + x = 5.802298395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.802298395 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.802298395 + -4 x = 5.802298395 + -4 Combine like terms: 5.802298395 + -4 = 1.802298395 x = 1.802298395 Simplifying x = 1.802298395

Subproblem 2

x + 4 = -5.802298395 Simplifying x + 4 = -5.802298395 Reorder the terms: 4 + x = -5.802298395 Solving 4 + x = -5.802298395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.802298395 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.802298395 + -4 x = -5.802298395 + -4 Combine like terms: -5.802298395 + -4 = -9.802298395 x = -9.802298395 Simplifying x = -9.802298395

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.802298395, -9.802298395}

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