a^2+7a-15=0

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Solution for a^2+7a-15=0 equation:


Simplifying
a2 + 7a + -15 = 0

Reorder the terms:
-15 + 7a + a2 = 0

Solving
-15 + 7a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 7a + 15 + a2 = 0 + 15

Reorder the terms:
-15 + 15 + 7a + a2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 7a + a2 = 0 + 15
7a + a2 = 0 + 15

Combine like terms: 0 + 15 = 15
7a + a2 = 15

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 = 15 + 12.25

Reorder the terms:
12.25 + 7a + a2 = 15 + 12.25

Combine like terms: 15 + 12.25 = 27.25
12.25 + 7a + a2 = 27.25

Factor a perfect square on the left side:
(a + 3.5)(a + 3.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(a + 3.5) equal to 5.220153254 and -5.220153254.

Subproblem 1

a + 3.5 = 5.220153254 Simplifying a + 3.5 = 5.220153254 Reorder the terms: 3.5 + a = 5.220153254 Solving 3.5 + a = 5.220153254 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 = 5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = 5.220153254 + -3.5 a = 5.220153254 + -3.5 Combine like terms: 5.220153254 + -3.5 = 1.720153254 a = 1.720153254 Simplifying a = 1.720153254

Subproblem 2

a + 3.5 = -5.220153254 Simplifying a + 3.5 = -5.220153254 Reorder the terms: 3.5 + a = -5.220153254 Solving 3.5 + a = -5.220153254 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 = -5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = -5.220153254 + -3.5 a = -5.220153254 + -3.5 Combine like terms: -5.220153254 + -3.5 = -8.720153254 a = -8.720153254 Simplifying a = -8.720153254

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.720153254, -8.720153254}

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