4a^2-12a+7=0

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Solution for 4a^2-12a+7=0 equation:


Simplifying
4a2 + -12a + 7 = 0

Reorder the terms:
7 + -12a + 4a2 = 0

Solving
7 + -12a + 4a2 = 0

Solving for variable 'a'.

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

Divide each side by '4'.
1.75 + -3a + a2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + -3a + -1.75 + a2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + -3a + a2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + -3a + a2 = 0 + -1.75
-3a + a2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
-3a + a2 = -1.75

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = -1.75 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -1.75 + 2.25

Combine like terms: -1.75 + 2.25 = 0.5
2.25 + -3a + a2 = 0.5

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(a + -1.5) equal to 0.707106781 and -0.707106781.

Subproblem 1

a + -1.5 = 0.707106781 Simplifying a + -1.5 = 0.707106781 Reorder the terms: -1.5 + a = 0.707106781 Solving -1.5 + a = 0.707106781 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = 0.707106781 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 0.707106781 + 1.5 a = 0.707106781 + 1.5 Combine like terms: 0.707106781 + 1.5 = 2.207106781 a = 2.207106781 Simplifying a = 2.207106781

Subproblem 2

a + -1.5 = -0.707106781 Simplifying a + -1.5 = -0.707106781 Reorder the terms: -1.5 + a = -0.707106781 Solving -1.5 + a = -0.707106781 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = -0.707106781 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -0.707106781 + 1.5 a = -0.707106781 + 1.5 Combine like terms: -0.707106781 + 1.5 = 0.792893219 a = 0.792893219 Simplifying a = 0.792893219

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.207106781, 0.792893219}

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