16x^2-26x+5=0

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Solution for 16x^2-26x+5=0 equation:


Simplifying
16x2 + -26x + 5 = 0

Reorder the terms:
5 + -26x + 16x2 = 0

Solving
5 + -26x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
0.3125 + -1.625x + x2 = 0

Move the constant term to the right:

Add '-0.3125' to each side of the equation.
0.3125 + -1.625x + -0.3125 + x2 = 0 + -0.3125

Reorder the terms:
0.3125 + -0.3125 + -1.625x + x2 = 0 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + -1.625x + x2 = 0 + -0.3125
-1.625x + x2 = 0 + -0.3125

Combine like terms: 0 + -0.3125 = -0.3125
-1.625x + x2 = -0.3125

The x term is -1.625x.  Take half its coefficient (-0.8125).
Square it (0.66015625) and add it to both sides.

Add '0.66015625' to each side of the equation.
-1.625x + 0.66015625 + x2 = -0.3125 + 0.66015625

Reorder the terms:
0.66015625 + -1.625x + x2 = -0.3125 + 0.66015625

Combine like terms: -0.3125 + 0.66015625 = 0.34765625
0.66015625 + -1.625x + x2 = 0.34765625

Factor a perfect square on the left side:
(x + -0.8125)(x + -0.8125) = 0.34765625

Calculate the square root of the right side: 0.589623821

Break this problem into two subproblems by setting 
(x + -0.8125) equal to 0.589623821 and -0.589623821.

Subproblem 1

x + -0.8125 = 0.589623821 Simplifying x + -0.8125 = 0.589623821 Reorder the terms: -0.8125 + x = 0.589623821 Solving -0.8125 + x = 0.589623821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + x = 0.589623821 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = 0.589623821 + 0.8125 x = 0.589623821 + 0.8125 Combine like terms: 0.589623821 + 0.8125 = 1.402123821 x = 1.402123821 Simplifying x = 1.402123821

Subproblem 2

x + -0.8125 = -0.589623821 Simplifying x + -0.8125 = -0.589623821 Reorder the terms: -0.8125 + x = -0.589623821 Solving -0.8125 + x = -0.589623821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + x = -0.589623821 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = -0.589623821 + 0.8125 x = -0.589623821 + 0.8125 Combine like terms: -0.589623821 + 0.8125 = 0.222876179 x = 0.222876179 Simplifying x = 0.222876179

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.402123821, 0.222876179}

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