x^2+9x-24+5=0

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Solution for x^2+9x-24+5=0 equation:


Simplifying
x2 + 9x + -24 + 5 = 0

Reorder the terms:
-24 + 5 + 9x + x2 = 0

Combine like terms: -24 + 5 = -19
-19 + 9x + x2 = 0

Solving
-19 + 9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 9x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + 9x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 9x + x2 = 0 + 19
9x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
9x + x2 = 19

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 19 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 19 + 20.25

Combine like terms: 19 + 20.25 = 39.25
20.25 + 9x + x2 = 39.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 39.25

Calculate the square root of the right side: 6.264982043

Break this problem into two subproblems by setting 
(x + 4.5) equal to 6.264982043 and -6.264982043.

Subproblem 1

x + 4.5 = 6.264982043 Simplifying x + 4.5 = 6.264982043 Reorder the terms: 4.5 + x = 6.264982043 Solving 4.5 + x = 6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 6.264982043 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 6.264982043 + -4.5 x = 6.264982043 + -4.5 Combine like terms: 6.264982043 + -4.5 = 1.764982043 x = 1.764982043 Simplifying x = 1.764982043

Subproblem 2

x + 4.5 = -6.264982043 Simplifying x + 4.5 = -6.264982043 Reorder the terms: 4.5 + x = -6.264982043 Solving 4.5 + x = -6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -6.264982043 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -6.264982043 + -4.5 x = -6.264982043 + -4.5 Combine like terms: -6.264982043 + -4.5 = -10.764982043 x = -10.764982043 Simplifying x = -10.764982043

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.764982043, -10.764982043}

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