x^2+7x=24

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Solution for x^2+7x=24 equation:


Simplifying
x2 + 7x = 24

Reorder the terms:
7x + x2 = 24

Solving
7x + x2 = 24

Solving for variable 'x'.

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

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

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 = 2.520797289 x = 2.520797289 Simplifying x = 2.520797289

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 = -9.520797289 x = -9.520797289 Simplifying x = -9.520797289

Solution

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

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