32a^2-19a=63

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Solution for 32a^2-19a=63 equation:


Simplifying
32a2 + -19a = 63

Reorder the terms:
-19a + 32a2 = 63

Solving
-19a + 32a2 = 63

Solving for variable 'a'.

Reorder the terms:
-63 + -19a + 32a2 = 63 + -63

Combine like terms: 63 + -63 = 0
-63 + -19a + 32a2 = 0

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

Divide each side by '32'.
-1.96875 + -0.59375a + a2 = 0

Move the constant term to the right:

Add '1.96875' to each side of the equation.
-1.96875 + -0.59375a + 1.96875 + a2 = 0 + 1.96875

Reorder the terms:
-1.96875 + 1.96875 + -0.59375a + a2 = 0 + 1.96875

Combine like terms: -1.96875 + 1.96875 = 0.00000
0.00000 + -0.59375a + a2 = 0 + 1.96875
-0.59375a + a2 = 0 + 1.96875

Combine like terms: 0 + 1.96875 = 1.96875
-0.59375a + a2 = 1.96875

The a term is -0.59375a.  Take half its coefficient (-0.296875).
Square it (0.08813476563) and add it to both sides.

Add '0.08813476563' to each side of the equation.
-0.59375a + 0.08813476563 + a2 = 1.96875 + 0.08813476563

Reorder the terms:
0.08813476563 + -0.59375a + a2 = 1.96875 + 0.08813476563

Combine like terms: 1.96875 + 0.08813476563 = 2.05688476563
0.08813476563 + -0.59375a + a2 = 2.05688476563

Factor a perfect square on the left side:
(a + -0.296875)(a + -0.296875) = 2.05688476563

Calculate the square root of the right side: 1.434184356

Break this problem into two subproblems by setting 
(a + -0.296875) equal to 1.434184356 and -1.434184356.

Subproblem 1

a + -0.296875 = 1.434184356 Simplifying a + -0.296875 = 1.434184356 Reorder the terms: -0.296875 + a = 1.434184356 Solving -0.296875 + a = 1.434184356 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.296875' to each side of the equation. -0.296875 + 0.296875 + a = 1.434184356 + 0.296875 Combine like terms: -0.296875 + 0.296875 = 0.000000 0.000000 + a = 1.434184356 + 0.296875 a = 1.434184356 + 0.296875 Combine like terms: 1.434184356 + 0.296875 = 1.731059356 a = 1.731059356 Simplifying a = 1.731059356

Subproblem 2

a + -0.296875 = -1.434184356 Simplifying a + -0.296875 = -1.434184356 Reorder the terms: -0.296875 + a = -1.434184356 Solving -0.296875 + a = -1.434184356 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.296875' to each side of the equation. -0.296875 + 0.296875 + a = -1.434184356 + 0.296875 Combine like terms: -0.296875 + 0.296875 = 0.000000 0.000000 + a = -1.434184356 + 0.296875 a = -1.434184356 + 0.296875 Combine like terms: -1.434184356 + 0.296875 = -1.137309356 a = -1.137309356 Simplifying a = -1.137309356

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.731059356, -1.137309356}

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