165x^2-15.68x-16.464=0

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Solution for 165x^2-15.68x-16.464=0 equation:


Simplifying
165x2 + -15.68x + -16.464 = 0

Reorder the terms:
-16.464 + -15.68x + 165x2 = 0

Solving
-16.464 + -15.68x + 165x2 = 0

Solving for variable 'x'.

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

Divide each side by '165'.
-0.09978181818 + -0.09503030303x + x2 = 0

Move the constant term to the right:

Add '0.09978181818' to each side of the equation.
-0.09978181818 + -0.09503030303x + 0.09978181818 + x2 = 0 + 0.09978181818

Reorder the terms:
-0.09978181818 + 0.09978181818 + -0.09503030303x + x2 = 0 + 0.09978181818

Combine like terms: -0.09978181818 + 0.09978181818 = 0.00000000000
0.00000000000 + -0.09503030303x + x2 = 0 + 0.09978181818
-0.09503030303x + x2 = 0 + 0.09978181818

Combine like terms: 0 + 0.09978181818 = 0.09978181818
-0.09503030303x + x2 = 0.09978181818

The x term is -0.09503030303x.  Take half its coefficient (-0.04751515152).
Square it (0.002257689624) and add it to both sides.

Add '0.002257689624' to each side of the equation.
-0.09503030303x + 0.002257689624 + x2 = 0.09978181818 + 0.002257689624

Reorder the terms:
0.002257689624 + -0.09503030303x + x2 = 0.09978181818 + 0.002257689624

Combine like terms: 0.09978181818 + 0.002257689624 = 0.102039507804
0.002257689624 + -0.09503030303x + x2 = 0.102039507804

Factor a perfect square on the left side:
(x + -0.04751515152)(x + -0.04751515152) = 0.102039507804

Calculate the square root of the right side: 0.319436234

Break this problem into two subproblems by setting 
(x + -0.04751515152) equal to 0.319436234 and -0.319436234.

Subproblem 1

x + -0.04751515152 = 0.319436234 Simplifying x + -0.04751515152 = 0.319436234 Reorder the terms: -0.04751515152 + x = 0.319436234 Solving -0.04751515152 + x = 0.319436234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04751515152' to each side of the equation. -0.04751515152 + 0.04751515152 + x = 0.319436234 + 0.04751515152 Combine like terms: -0.04751515152 + 0.04751515152 = 0.00000000000 0.00000000000 + x = 0.319436234 + 0.04751515152 x = 0.319436234 + 0.04751515152 Combine like terms: 0.319436234 + 0.04751515152 = 0.36695138552 x = 0.36695138552 Simplifying x = 0.36695138552

Subproblem 2

x + -0.04751515152 = -0.319436234 Simplifying x + -0.04751515152 = -0.319436234 Reorder the terms: -0.04751515152 + x = -0.319436234 Solving -0.04751515152 + x = -0.319436234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04751515152' to each side of the equation. -0.04751515152 + 0.04751515152 + x = -0.319436234 + 0.04751515152 Combine like terms: -0.04751515152 + 0.04751515152 = 0.00000000000 0.00000000000 + x = -0.319436234 + 0.04751515152 x = -0.319436234 + 0.04751515152 Combine like terms: -0.319436234 + 0.04751515152 = -0.27192108248 x = -0.27192108248 Simplifying x = -0.27192108248

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.36695138552, -0.27192108248}

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