a^2-7a=12

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Solution for a^2-7a=12 equation:


Simplifying
a2 + -7a = 12

Reorder the terms:
-7a + a2 = 12

Solving
-7a + a2 = 12

Solving for variable 'a'.

Reorder the terms:
-12 + -7a + a2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -7a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -7a + 12 + a2 = 0 + 12

Reorder the terms:
-12 + 12 + -7a + a2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -7a + a2 = 0 + 12
-7a + a2 = 0 + 12

Combine like terms: 0 + 12 = 12
-7a + a2 = 12

The a term is -7a.  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.
-7a + 12.25 + a2 = 12 + 12.25

Reorder the terms:
12.25 + -7a + a2 = 12 + 12.25

Combine like terms: 12 + 12.25 = 24.25
12.25 + -7a + a2 = 24.25

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

Calculate the square root of the right side: 4.924428901

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

Subproblem 1

a + -3.5 = 4.924428901 Simplifying a + -3.5 = 4.924428901 Reorder the terms: -3.5 + a = 4.924428901 Solving -3.5 + a = 4.924428901 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = 4.924428901 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = 4.924428901 + 3.5 a = 4.924428901 + 3.5 Combine like terms: 4.924428901 + 3.5 = 8.424428901 a = 8.424428901 Simplifying a = 8.424428901

Subproblem 2

a + -3.5 = -4.924428901 Simplifying a + -3.5 = -4.924428901 Reorder the terms: -3.5 + a = -4.924428901 Solving -3.5 + a = -4.924428901 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = -4.924428901 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = -4.924428901 + 3.5 a = -4.924428901 + 3.5 Combine like terms: -4.924428901 + 3.5 = -1.424428901 a = -1.424428901 Simplifying a = -1.424428901

Solution

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

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