1.34a^2-2a=15

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Solution for 1.34a^2-2a=15 equation:


Simplifying
1.34a2 + -2a = 15

Reorder the terms:
-2a + 1.34a2 = 15

Solving
-2a + 1.34a2 = 15

Solving for variable 'a'.

Reorder the terms:
-15 + -2a + 1.34a2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -2a + 1.34a2 = 0

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

Divide each side by '1.34'.
-11.19402985 + -1.492537313a + a2 = 0

Move the constant term to the right:

Add '11.19402985' to each side of the equation.
-11.19402985 + -1.492537313a + 11.19402985 + a2 = 0 + 11.19402985

Reorder the terms:
-11.19402985 + 11.19402985 + -1.492537313a + a2 = 0 + 11.19402985

Combine like terms: -11.19402985 + 11.19402985 = 0.00000000
0.00000000 + -1.492537313a + a2 = 0 + 11.19402985
-1.492537313a + a2 = 0 + 11.19402985

Combine like terms: 0 + 11.19402985 = 11.19402985
-1.492537313a + a2 = 11.19402985

The a term is -1.492537313a.  Take half its coefficient (-0.7462686565).
Square it (0.5569169077) and add it to both sides.

Add '0.5569169077' to each side of the equation.
-1.492537313a + 0.5569169077 + a2 = 11.19402985 + 0.5569169077

Reorder the terms:
0.5569169077 + -1.492537313a + a2 = 11.19402985 + 0.5569169077

Combine like terms: 11.19402985 + 0.5569169077 = 11.7509467577
0.5569169077 + -1.492537313a + a2 = 11.7509467577

Factor a perfect square on the left side:
(a + -0.7462686565)(a + -0.7462686565) = 11.7509467577

Calculate the square root of the right side: 3.427965396

Break this problem into two subproblems by setting 
(a + -0.7462686565) equal to 3.427965396 and -3.427965396.

Subproblem 1

a + -0.7462686565 = 3.427965396 Simplifying a + -0.7462686565 = 3.427965396 Reorder the terms: -0.7462686565 + a = 3.427965396 Solving -0.7462686565 + a = 3.427965396 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.7462686565' to each side of the equation. -0.7462686565 + 0.7462686565 + a = 3.427965396 + 0.7462686565 Combine like terms: -0.7462686565 + 0.7462686565 = 0.0000000000 0.0000000000 + a = 3.427965396 + 0.7462686565 a = 3.427965396 + 0.7462686565 Combine like terms: 3.427965396 + 0.7462686565 = 4.1742340525 a = 4.1742340525 Simplifying a = 4.1742340525

Subproblem 2

a + -0.7462686565 = -3.427965396 Simplifying a + -0.7462686565 = -3.427965396 Reorder the terms: -0.7462686565 + a = -3.427965396 Solving -0.7462686565 + a = -3.427965396 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.7462686565' to each side of the equation. -0.7462686565 + 0.7462686565 + a = -3.427965396 + 0.7462686565 Combine like terms: -0.7462686565 + 0.7462686565 = 0.0000000000 0.0000000000 + a = -3.427965396 + 0.7462686565 a = -3.427965396 + 0.7462686565 Combine like terms: -3.427965396 + 0.7462686565 = -2.6816967395 a = -2.6816967395 Simplifying a = -2.6816967395

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.1742340525, -2.6816967395}

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