a^2-14a=24

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Solution for a^2-14a=24 equation:


Simplifying
a2 + -14a = 24

Reorder the terms:
-14a + a2 = 24

Solving
-14a + a2 = 24

Solving for variable 'a'.

Reorder the terms:
-24 + -14a + a2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -14a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -14a + 24 + a2 = 0 + 24

Reorder the terms:
-24 + 24 + -14a + a2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -14a + a2 = 0 + 24
-14a + a2 = 0 + 24

Combine like terms: 0 + 24 = 24
-14a + a2 = 24

The a term is -14a.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14a + 49 + a2 = 24 + 49

Reorder the terms:
49 + -14a + a2 = 24 + 49

Combine like terms: 24 + 49 = 73
49 + -14a + a2 = 73

Factor a perfect square on the left side:
(a + -7)(a + -7) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(a + -7) equal to 8.544003745 and -8.544003745.

Subproblem 1

a + -7 = 8.544003745 Simplifying a + -7 = 8.544003745 Reorder the terms: -7 + a = 8.544003745 Solving -7 + a = 8.544003745 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = 8.544003745 + 7 Combine like terms: -7 + 7 = 0 0 + a = 8.544003745 + 7 a = 8.544003745 + 7 Combine like terms: 8.544003745 + 7 = 15.544003745 a = 15.544003745 Simplifying a = 15.544003745

Subproblem 2

a + -7 = -8.544003745 Simplifying a + -7 = -8.544003745 Reorder the terms: -7 + a = -8.544003745 Solving -7 + a = -8.544003745 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = -8.544003745 + 7 Combine like terms: -7 + 7 = 0 0 + a = -8.544003745 + 7 a = -8.544003745 + 7 Combine like terms: -8.544003745 + 7 = -1.544003745 a = -1.544003745 Simplifying a = -1.544003745

Solution

The solution to the problem is based on the solutions from the subproblems. a = {15.544003745, -1.544003745}

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