7x+24=x^2+12

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Solution for 7x+24=x^2+12 equation:


Simplifying
7x + 24 = x2 + 12

Reorder the terms:
24 + 7x = x2 + 12

Reorder the terms:
24 + 7x = 12 + x2

Solving
24 + 7x = 12 + x2

Solving for variable 'x'.

Reorder the terms:
24 + -12 + 7x + -1x2 = 12 + x2 + -12 + -1x2

Combine like terms: 24 + -12 = 12
12 + 7x + -1x2 = 12 + x2 + -12 + -1x2

Reorder the terms:
12 + 7x + -1x2 = 12 + -12 + x2 + -1x2

Combine like terms: 12 + -12 = 0
12 + 7x + -1x2 = 0 + x2 + -1x2
12 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + 7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-12 + -7x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -7x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -7x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -7x + x2 = 0 + 12
-7x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-7x + x2 = 12

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 = 12 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 12 + 12.25

Combine like terms: 12 + 12.25 = 24.25
12.25 + -7x + x2 = 24.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + -3.5) equal to 4.924428901 and -4.924428901.

Subproblem 1

x + -3.5 = 4.924428901 Simplifying x + -3.5 = 4.924428901 Reorder the terms: -3.5 + x = 4.924428901 Solving -3.5 + x = 4.924428901 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 = 4.924428901 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.924428901 + 3.5 x = 4.924428901 + 3.5 Combine like terms: 4.924428901 + 3.5 = 8.424428901 x = 8.424428901 Simplifying x = 8.424428901

Subproblem 2

x + -3.5 = -4.924428901 Simplifying x + -3.5 = -4.924428901 Reorder the terms: -3.5 + x = -4.924428901 Solving -3.5 + x = -4.924428901 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 = -4.924428901 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.924428901 + 3.5 x = -4.924428901 + 3.5 Combine like terms: -4.924428901 + 3.5 = -1.424428901 x = -1.424428901 Simplifying x = -1.424428901

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.424428901, -1.424428901}

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