a^2-15a=-42

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Solution for a^2-15a=-42 equation:


Simplifying
a2 + -15a = -42

Reorder the terms:
-15a + a2 = -42

Solving
-15a + a2 = -42

Solving for variable 'a'.

Reorder the terms:
42 + -15a + a2 = -42 + 42

Combine like terms: -42 + 42 = 0
42 + -15a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + -15a + -42 + a2 = 0 + -42

Reorder the terms:
42 + -42 + -15a + a2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -15a + a2 = 0 + -42
-15a + a2 = 0 + -42

Combine like terms: 0 + -42 = -42
-15a + a2 = -42

The a term is -15a.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15a + 56.25 + a2 = -42 + 56.25

Reorder the terms:
56.25 + -15a + a2 = -42 + 56.25

Combine like terms: -42 + 56.25 = 14.25
56.25 + -15a + a2 = 14.25

Factor a perfect square on the left side:
(a + -7.5)(a + -7.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(a + -7.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

a + -7.5 = 3.774917218 Simplifying a + -7.5 = 3.774917218 Reorder the terms: -7.5 + a = 3.774917218 Solving -7.5 + a = 3.774917218 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + a = 3.774917218 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + a = 3.774917218 + 7.5 a = 3.774917218 + 7.5 Combine like terms: 3.774917218 + 7.5 = 11.274917218 a = 11.274917218 Simplifying a = 11.274917218

Subproblem 2

a + -7.5 = -3.774917218 Simplifying a + -7.5 = -3.774917218 Reorder the terms: -7.5 + a = -3.774917218 Solving -7.5 + a = -3.774917218 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + a = -3.774917218 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + a = -3.774917218 + 7.5 a = -3.774917218 + 7.5 Combine like terms: -3.774917218 + 7.5 = 3.725082782 a = 3.725082782 Simplifying a = 3.725082782

Solution

The solution to the problem is based on the solutions from the subproblems. a = {11.274917218, 3.725082782}

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