a^2+2a-75=0

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Solution for a^2+2a-75=0 equation:


Simplifying
a2 + 2a + -75 = 0

Reorder the terms:
-75 + 2a + a2 = 0

Solving
-75 + 2a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 2a + 75 + a2 = 0 + 75

Reorder the terms:
-75 + 75 + 2a + a2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 2a + a2 = 0 + 75
2a + a2 = 0 + 75

Combine like terms: 0 + 75 = 75
2a + a2 = 75

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = 75 + 1

Reorder the terms:
1 + 2a + a2 = 75 + 1

Combine like terms: 75 + 1 = 76
1 + 2a + a2 = 76

Factor a perfect square on the left side:
(a + 1)(a + 1) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(a + 1) equal to 8.717797887 and -8.717797887.

Subproblem 1

a + 1 = 8.717797887 Simplifying a + 1 = 8.717797887 Reorder the terms: 1 + a = 8.717797887 Solving 1 + a = 8.717797887 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 8.717797887 + -1 Combine like terms: 1 + -1 = 0 0 + a = 8.717797887 + -1 a = 8.717797887 + -1 Combine like terms: 8.717797887 + -1 = 7.717797887 a = 7.717797887 Simplifying a = 7.717797887

Subproblem 2

a + 1 = -8.717797887 Simplifying a + 1 = -8.717797887 Reorder the terms: 1 + a = -8.717797887 Solving 1 + a = -8.717797887 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -8.717797887 + -1 Combine like terms: 1 + -1 = 0 0 + a = -8.717797887 + -1 a = -8.717797887 + -1 Combine like terms: -8.717797887 + -1 = -9.717797887 a = -9.717797887 Simplifying a = -9.717797887

Solution

The solution to the problem is based on the solutions from the subproblems. a = {7.717797887, -9.717797887}

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