16a^2-24a+7=0

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Solution for 16a^2-24a+7=0 equation:


Simplifying
16a2 + -24a + 7 = 0

Reorder the terms:
7 + -24a + 16a2 = 0

Solving
7 + -24a + 16a2 = 0

Solving for variable 'a'.

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

Divide each side by '16'.
0.4375 + -1.5a + a2 = 0

Move the constant term to the right:

Add '-0.4375' to each side of the equation.
0.4375 + -1.5a + -0.4375 + a2 = 0 + -0.4375

Reorder the terms:
0.4375 + -0.4375 + -1.5a + a2 = 0 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + -1.5a + a2 = 0 + -0.4375
-1.5a + a2 = 0 + -0.4375

Combine like terms: 0 + -0.4375 = -0.4375
-1.5a + a2 = -0.4375

The a term is -1.5a.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5a + 0.5625 + a2 = -0.4375 + 0.5625

Reorder the terms:
0.5625 + -1.5a + a2 = -0.4375 + 0.5625

Combine like terms: -0.4375 + 0.5625 = 0.125
0.5625 + -1.5a + a2 = 0.125

Factor a perfect square on the left side:
(a + -0.75)(a + -0.75) = 0.125

Calculate the square root of the right side: 0.353553391

Break this problem into two subproblems by setting 
(a + -0.75) equal to 0.353553391 and -0.353553391.

Subproblem 1

a + -0.75 = 0.353553391 Simplifying a + -0.75 = 0.353553391 Reorder the terms: -0.75 + a = 0.353553391 Solving -0.75 + a = 0.353553391 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = 0.353553391 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = 0.353553391 + 0.75 a = 0.353553391 + 0.75 Combine like terms: 0.353553391 + 0.75 = 1.103553391 a = 1.103553391 Simplifying a = 1.103553391

Subproblem 2

a + -0.75 = -0.353553391 Simplifying a + -0.75 = -0.353553391 Reorder the terms: -0.75 + a = -0.353553391 Solving -0.75 + a = -0.353553391 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = -0.353553391 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = -0.353553391 + 0.75 a = -0.353553391 + 0.75 Combine like terms: -0.353553391 + 0.75 = 0.396446609 a = 0.396446609 Simplifying a = 0.396446609

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.103553391, 0.396446609}

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