a^2+10a-65=4

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Solution for a^2+10a-65=4 equation:


Simplifying
a2 + 10a + -65 = 4

Reorder the terms:
-65 + 10a + a2 = 4

Solving
-65 + 10a + a2 = 4

Solving for variable 'a'.

Reorder the terms:
-65 + -4 + 10a + a2 = 4 + -4

Combine like terms: -65 + -4 = -69
-69 + 10a + a2 = 4 + -4

Combine like terms: 4 + -4 = 0
-69 + 10a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '69' to each side of the equation.
-69 + 10a + 69 + a2 = 0 + 69

Reorder the terms:
-69 + 69 + 10a + a2 = 0 + 69

Combine like terms: -69 + 69 = 0
0 + 10a + a2 = 0 + 69
10a + a2 = 0 + 69

Combine like terms: 0 + 69 = 69
10a + a2 = 69

The a term is 10a.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10a + 25 + a2 = 69 + 25

Reorder the terms:
25 + 10a + a2 = 69 + 25

Combine like terms: 69 + 25 = 94
25 + 10a + a2 = 94

Factor a perfect square on the left side:
(a + 5)(a + 5) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(a + 5) equal to 9.695359715 and -9.695359715.

Subproblem 1

a + 5 = 9.695359715 Simplifying a + 5 = 9.695359715 Reorder the terms: 5 + a = 9.695359715 Solving 5 + a = 9.695359715 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 9.695359715 + -5 Combine like terms: 5 + -5 = 0 0 + a = 9.695359715 + -5 a = 9.695359715 + -5 Combine like terms: 9.695359715 + -5 = 4.695359715 a = 4.695359715 Simplifying a = 4.695359715

Subproblem 2

a + 5 = -9.695359715 Simplifying a + 5 = -9.695359715 Reorder the terms: 5 + a = -9.695359715 Solving 5 + a = -9.695359715 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = -9.695359715 + -5 Combine like terms: 5 + -5 = 0 0 + a = -9.695359715 + -5 a = -9.695359715 + -5 Combine like terms: -9.695359715 + -5 = -14.695359715 a = -14.695359715 Simplifying a = -14.695359715

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.695359715, -14.695359715}

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