8a^2-16a+3=4

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Solution for 8a^2-16a+3=4 equation:


Simplifying
8a2 + -16a + 3 = 4

Reorder the terms:
3 + -16a + 8a2 = 4

Solving
3 + -16a + 8a2 = 4

Solving for variable 'a'.

Reorder the terms:
3 + -4 + -16a + 8a2 = 4 + -4

Combine like terms: 3 + -4 = -1
-1 + -16a + 8a2 = 4 + -4

Combine like terms: 4 + -4 = 0
-1 + -16a + 8a2 = 0

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

Divide each side by '8'.
-0.125 + -2a + a2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -2a + 0.125 + a2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -2a + a2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -2a + a2 = 0 + 0.125
-2a + a2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-2a + a2 = 0.125

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 = 0.125 + 1

Reorder the terms:
1 + -2a + a2 = 0.125 + 1

Combine like terms: 0.125 + 1 = 1.125
1 + -2a + a2 = 1.125

Factor a perfect square on the left side:
(a + -1)(a + -1) = 1.125

Calculate the square root of the right side: 1.060660172

Break this problem into two subproblems by setting 
(a + -1) equal to 1.060660172 and -1.060660172.

Subproblem 1

a + -1 = 1.060660172 Simplifying a + -1 = 1.060660172 Reorder the terms: -1 + a = 1.060660172 Solving -1 + a = 1.060660172 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 = 1.060660172 + 1 Combine like terms: -1 + 1 = 0 0 + a = 1.060660172 + 1 a = 1.060660172 + 1 Combine like terms: 1.060660172 + 1 = 2.060660172 a = 2.060660172 Simplifying a = 2.060660172

Subproblem 2

a + -1 = -1.060660172 Simplifying a + -1 = -1.060660172 Reorder the terms: -1 + a = -1.060660172 Solving -1 + a = -1.060660172 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 = -1.060660172 + 1 Combine like terms: -1 + 1 = 0 0 + a = -1.060660172 + 1 a = -1.060660172 + 1 Combine like terms: -1.060660172 + 1 = -0.060660172 a = -0.060660172 Simplifying a = -0.060660172

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.060660172, -0.060660172}

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