2a^2+a=7

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Solution for 2a^2+a=7 equation:


Simplifying
2a2 + a = 7

Reorder the terms:
a + 2a2 = 7

Solving
a + 2a2 = 7

Solving for variable 'a'.

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

Combine like terms: 7 + -7 = 0
-7 + a + 2a2 = 0

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

Divide each side by '2'.
-3.5 + 0.5a + a2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 0.5a + 3.5 + a2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 0.5a + a2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 0.5a + a2 = 0 + 3.5
0.5a + a2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
0.5a + a2 = 3.5

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5a + 0.25 + a2 = 3.5 + 0.25

Reorder the terms:
0.25 + 0.5a + a2 = 3.5 + 0.25

Combine like terms: 3.5 + 0.25 = 3.75
0.25 + 0.5a + a2 = 3.75

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(a + 0.5) equal to 1.936491673 and -1.936491673.

Subproblem 1

a + 0.5 = 1.936491673 Simplifying a + 0.5 = 1.936491673 Reorder the terms: 0.5 + a = 1.936491673 Solving 0.5 + a = 1.936491673 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 1.936491673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 1.936491673 + -0.5 a = 1.936491673 + -0.5 Combine like terms: 1.936491673 + -0.5 = 1.436491673 a = 1.436491673 Simplifying a = 1.436491673

Subproblem 2

a + 0.5 = -1.936491673 Simplifying a + 0.5 = -1.936491673 Reorder the terms: 0.5 + a = -1.936491673 Solving 0.5 + a = -1.936491673 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -1.936491673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -1.936491673 + -0.5 a = -1.936491673 + -0.5 Combine like terms: -1.936491673 + -0.5 = -2.436491673 a = -2.436491673 Simplifying a = -2.436491673

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.436491673, -2.436491673}

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