5x^2-16x-3=0

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Solution for 5x^2-16x-3=0 equation:


Simplifying
5x2 + -16x + -3 = 0

Reorder the terms:
-3 + -16x + 5x2 = 0

Solving
-3 + -16x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-0.6 + -3.2x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -3.2x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -3.2x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -3.2x + x2 = 0 + 0.6
-3.2x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-3.2x + x2 = 0.6

The x term is -3.2x.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2x + 2.56 + x2 = 0.6 + 2.56

Reorder the terms:
2.56 + -3.2x + x2 = 0.6 + 2.56

Combine like terms: 0.6 + 2.56 = 3.16
2.56 + -3.2x + x2 = 3.16

Factor a perfect square on the left side:
(x + -1.6)(x + -1.6) = 3.16

Calculate the square root of the right side: 1.777638883

Break this problem into two subproblems by setting 
(x + -1.6) equal to 1.777638883 and -1.777638883.

Subproblem 1

x + -1.6 = 1.777638883 Simplifying x + -1.6 = 1.777638883 Reorder the terms: -1.6 + x = 1.777638883 Solving -1.6 + x = 1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 1.777638883 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 1.777638883 + 1.6 x = 1.777638883 + 1.6 Combine like terms: 1.777638883 + 1.6 = 3.377638883 x = 3.377638883 Simplifying x = 3.377638883

Subproblem 2

x + -1.6 = -1.777638883 Simplifying x + -1.6 = -1.777638883 Reorder the terms: -1.6 + x = -1.777638883 Solving -1.6 + x = -1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -1.777638883 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -1.777638883 + 1.6 x = -1.777638883 + 1.6 Combine like terms: -1.777638883 + 1.6 = -0.177638883 x = -0.177638883 Simplifying x = -0.177638883

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.377638883, -0.177638883}

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