5x^2+20x-24=0

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Solution for 5x^2+20x-24=0 equation:


Simplifying
5x2 + 20x + -24 = 0

Reorder the terms:
-24 + 20x + 5x2 = 0

Solving
-24 + 20x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-4.8 + 4x + x2 = 0

Move the constant term to the right:

Add '4.8' to each side of the equation.
-4.8 + 4x + 4.8 + x2 = 0 + 4.8

Reorder the terms:
-4.8 + 4.8 + 4x + x2 = 0 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + 4x + x2 = 0 + 4.8
4x + x2 = 0 + 4.8

Combine like terms: 0 + 4.8 = 4.8
4x + x2 = 4.8

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 4.8 + 4

Reorder the terms:
4 + 4x + x2 = 4.8 + 4

Combine like terms: 4.8 + 4 = 8.8
4 + 4x + x2 = 8.8

Factor a perfect square on the left side:
(x + 2)(x + 2) = 8.8

Calculate the square root of the right side: 2.966479395

Break this problem into two subproblems by setting 
(x + 2) equal to 2.966479395 and -2.966479395.

Subproblem 1

x + 2 = 2.966479395 Simplifying x + 2 = 2.966479395 Reorder the terms: 2 + x = 2.966479395 Solving 2 + x = 2.966479395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.966479395 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.966479395 + -2 x = 2.966479395 + -2 Combine like terms: 2.966479395 + -2 = 0.966479395 x = 0.966479395 Simplifying x = 0.966479395

Subproblem 2

x + 2 = -2.966479395 Simplifying x + 2 = -2.966479395 Reorder the terms: 2 + x = -2.966479395 Solving 2 + x = -2.966479395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.966479395 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.966479395 + -2 x = -2.966479395 + -2 Combine like terms: -2.966479395 + -2 = -4.966479395 x = -4.966479395 Simplifying x = -4.966479395

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.966479395, -4.966479395}

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