a^2+5a-7=0

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Solution for a^2+5a-7=0 equation:


Simplifying
a2 + 5a + -7 = 0

Reorder the terms:
-7 + 5a + a2 = 0

Solving
-7 + 5a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 5a + 7 + a2 = 0 + 7

Reorder the terms:
-7 + 7 + 5a + a2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 5a + a2 = 0 + 7
5a + a2 = 0 + 7

Combine like terms: 0 + 7 = 7
5a + a2 = 7

The a term is 5a.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5a + 6.25 + a2 = 7 + 6.25

Reorder the terms:
6.25 + 5a + a2 = 7 + 6.25

Combine like terms: 7 + 6.25 = 13.25
6.25 + 5a + a2 = 13.25

Factor a perfect square on the left side:
(a + 2.5)(a + 2.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(a + 2.5) equal to 3.640054945 and -3.640054945.

Subproblem 1

a + 2.5 = 3.640054945 Simplifying a + 2.5 = 3.640054945 Reorder the terms: 2.5 + a = 3.640054945 Solving 2.5 + a = 3.640054945 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = 3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 3.640054945 + -2.5 a = 3.640054945 + -2.5 Combine like terms: 3.640054945 + -2.5 = 1.140054945 a = 1.140054945 Simplifying a = 1.140054945

Subproblem 2

a + 2.5 = -3.640054945 Simplifying a + 2.5 = -3.640054945 Reorder the terms: 2.5 + a = -3.640054945 Solving 2.5 + a = -3.640054945 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = -3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -3.640054945 + -2.5 a = -3.640054945 + -2.5 Combine like terms: -3.640054945 + -2.5 = -6.140054945 a = -6.140054945 Simplifying a = -6.140054945

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.140054945, -6.140054945}

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