x^2-7x-24=0

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Solution for x^2-7x-24=0 equation:


Simplifying
x2 + -7x + -24 = 0

Reorder the terms:
-24 + -7x + x2 = 0

Solving
-24 + -7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -7x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -7x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -7x + x2 = 0 + 24
-7x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-7x + x2 = 24

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 24 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 24 + 12.25

Combine like terms: 24 + 12.25 = 36.25
12.25 + -7x + x2 = 36.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x + -3.5) equal to 6.020797289 and -6.020797289.


Subproblem 1
x + -3.5 = 6.020797289

Simplifying
x + -3.5 = 6.020797289

Reorder the terms:
-3.5 + x = 6.020797289

Solving
-3.5 + x = 6.020797289

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 6.020797289 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 6.020797289 + 3.5
x = 6.020797289 + 3.5

Combine like terms: 6.020797289 + 3.5 = 9.520797289
x = 9.520797289

Simplifying
x = 9.520797289


Subproblem 2
x + -3.5 = -6.020797289

Simplifying
x + -3.5 = -6.020797289

Reorder the terms:
-3.5 + x = -6.020797289

Solving
-3.5 + x = -6.020797289

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -6.020797289 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -6.020797289 + 3.5
x = -6.020797289 + 3.5

Combine like terms: -6.020797289 + 3.5 = -2.520797289
x = -2.520797289

Simplifying
x = -2.520797289


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.520797289, -2.520797289}

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