32x^2+32x-17=0

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Solution for 32x^2+32x-17=0 equation:


Simplifying
32x2 + 32x + -17 = 0

Reorder the terms:
-17 + 32x + 32x2 = 0

Solving
-17 + 32x + 32x2 = 0

Solving for variable 'x'.

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

Divide each side by '32'.
-0.53125 + x + x2 = 0

Move the constant term to the right:

Add '0.53125' to each side of the equation.
-0.53125 + x + 0.53125 + x2 = 0 + 0.53125

Reorder the terms:
-0.53125 + 0.53125 + x + x2 = 0 + 0.53125

Combine like terms: -0.53125 + 0.53125 = 0.00000
0.00000 + x + x2 = 0 + 0.53125
x + x2 = 0 + 0.53125

Combine like terms: 0 + 0.53125 = 0.53125
x + x2 = 0.53125

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 0.53125 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.53125 + 0.25

Combine like terms: 0.53125 + 0.25 = 0.78125
1.25 + x2 = 0.78125

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.78125

Calculate the square root of the right side: 0.883883476

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.883883476 and -0.883883476.

Subproblem 1

x + 0.5 = 0.883883476 Simplifying x + 0.5 = 0.883883476 Reorder the terms: 0.5 + x = 0.883883476 Solving 0.5 + x = 0.883883476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.883883476 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.883883476 + -0.5 x = 0.883883476 + -0.5 Combine like terms: 0.883883476 + -0.5 = 0.383883476 x = 0.383883476 Simplifying x = 0.383883476

Subproblem 2

x + 0.5 = -0.883883476 Simplifying x + 0.5 = -0.883883476 Reorder the terms: 0.5 + x = -0.883883476 Solving 0.5 + x = -0.883883476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.883883476 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.883883476 + -0.5 x = -0.883883476 + -0.5 Combine like terms: -0.883883476 + -0.5 = -1.383883476 x = -1.383883476 Simplifying x = -1.383883476

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.383883476, -1.383883476}

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