2a^2+7a-10=0

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Solution for 2a^2+7a-10=0 equation:


Simplifying
2a2 + 7a + -10 = 0

Reorder the terms:
-10 + 7a + 2a2 = 0

Solving
-10 + 7a + 2a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-5 + 3.5a + a2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 3.5a + 5 + a2 = 0 + 5

Reorder the terms:
-5 + 5 + 3.5a + a2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3.5a + a2 = 0 + 5
3.5a + a2 = 0 + 5

Combine like terms: 0 + 5 = 5
3.5a + a2 = 5

The a term is 3.5a.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5a + 3.0625 + a2 = 5 + 3.0625

Reorder the terms:
3.0625 + 3.5a + a2 = 5 + 3.0625

Combine like terms: 5 + 3.0625 = 8.0625
3.0625 + 3.5a + a2 = 8.0625

Factor a perfect square on the left side:
(a + 1.75)(a + 1.75) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(a + 1.75) equal to 2.839454173 and -2.839454173.

Subproblem 1

a + 1.75 = 2.839454173 Simplifying a + 1.75 = 2.839454173 Reorder the terms: 1.75 + a = 2.839454173 Solving 1.75 + a = 2.839454173 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + a = 2.839454173 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + a = 2.839454173 + -1.75 a = 2.839454173 + -1.75 Combine like terms: 2.839454173 + -1.75 = 1.089454173 a = 1.089454173 Simplifying a = 1.089454173

Subproblem 2

a + 1.75 = -2.839454173 Simplifying a + 1.75 = -2.839454173 Reorder the terms: 1.75 + a = -2.839454173 Solving 1.75 + a = -2.839454173 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + a = -2.839454173 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + a = -2.839454173 + -1.75 a = -2.839454173 + -1.75 Combine like terms: -2.839454173 + -1.75 = -4.589454173 a = -4.589454173 Simplifying a = -4.589454173

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.089454173, -4.589454173}

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