17x^2+32x-30=0

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Solution for 17x^2+32x-30=0 equation:


Simplifying
17x2 + 32x + -30 = 0

Reorder the terms:
-30 + 32x + 17x2 = 0

Solving
-30 + 32x + 17x2 = 0

Solving for variable 'x'.

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

Divide each side by '17'.
-1.764705882 + 1.882352941x + x2 = 0

Move the constant term to the right:

Add '1.764705882' to each side of the equation.
-1.764705882 + 1.882352941x + 1.764705882 + x2 = 0 + 1.764705882

Reorder the terms:
-1.764705882 + 1.764705882 + 1.882352941x + x2 = 0 + 1.764705882

Combine like terms: -1.764705882 + 1.764705882 = 0.000000000
0.000000000 + 1.882352941x + x2 = 0 + 1.764705882
1.882352941x + x2 = 0 + 1.764705882

Combine like terms: 0 + 1.764705882 = 1.764705882
1.882352941x + x2 = 1.764705882

The x term is 1.882352941x.  Take half its coefficient (0.9411764705).
Square it (0.8858131486) and add it to both sides.

Add '0.8858131486' to each side of the equation.
1.882352941x + 0.8858131486 + x2 = 1.764705882 + 0.8858131486

Reorder the terms:
0.8858131486 + 1.882352941x + x2 = 1.764705882 + 0.8858131486

Combine like terms: 1.764705882 + 0.8858131486 = 2.6505190306
0.8858131486 + 1.882352941x + x2 = 2.6505190306

Factor a perfect square on the left side:
(x + 0.9411764705)(x + 0.9411764705) = 2.6505190306

Calculate the square root of the right side: 1.628041471

Break this problem into two subproblems by setting 
(x + 0.9411764705) equal to 1.628041471 and -1.628041471.

Subproblem 1

x + 0.9411764705 = 1.628041471 Simplifying x + 0.9411764705 = 1.628041471 Reorder the terms: 0.9411764705 + x = 1.628041471 Solving 0.9411764705 + x = 1.628041471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9411764705' to each side of the equation. 0.9411764705 + -0.9411764705 + x = 1.628041471 + -0.9411764705 Combine like terms: 0.9411764705 + -0.9411764705 = 0.0000000000 0.0000000000 + x = 1.628041471 + -0.9411764705 x = 1.628041471 + -0.9411764705 Combine like terms: 1.628041471 + -0.9411764705 = 0.6868650005 x = 0.6868650005 Simplifying x = 0.6868650005

Subproblem 2

x + 0.9411764705 = -1.628041471 Simplifying x + 0.9411764705 = -1.628041471 Reorder the terms: 0.9411764705 + x = -1.628041471 Solving 0.9411764705 + x = -1.628041471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9411764705' to each side of the equation. 0.9411764705 + -0.9411764705 + x = -1.628041471 + -0.9411764705 Combine like terms: 0.9411764705 + -0.9411764705 = 0.0000000000 0.0000000000 + x = -1.628041471 + -0.9411764705 x = -1.628041471 + -0.9411764705 Combine like terms: -1.628041471 + -0.9411764705 = -2.5692179415 x = -2.5692179415 Simplifying x = -2.5692179415

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6868650005, -2.5692179415}

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