17x^2+61x+40=0

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Solution for 17x^2+61x+40=0 equation:


Simplifying
17x2 + 61x + 40 = 0

Reorder the terms:
40 + 61x + 17x2 = 0

Solving
40 + 61x + 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'.
2.352941176 + 3.588235294x + x2 = 0

Move the constant term to the right:

Add '-2.352941176' to each side of the equation.
2.352941176 + 3.588235294x + -2.352941176 + x2 = 0 + -2.352941176

Reorder the terms:
2.352941176 + -2.352941176 + 3.588235294x + x2 = 0 + -2.352941176

Combine like terms: 2.352941176 + -2.352941176 = 0.000000000
0.000000000 + 3.588235294x + x2 = 0 + -2.352941176
3.588235294x + x2 = 0 + -2.352941176

Combine like terms: 0 + -2.352941176 = -2.352941176
3.588235294x + x2 = -2.352941176

The x term is 3.588235294x.  Take half its coefficient (1.794117647).
Square it (3.218858131) and add it to both sides.

Add '3.218858131' to each side of the equation.
3.588235294x + 3.218858131 + x2 = -2.352941176 + 3.218858131

Reorder the terms:
3.218858131 + 3.588235294x + x2 = -2.352941176 + 3.218858131

Combine like terms: -2.352941176 + 3.218858131 = 0.865916955
3.218858131 + 3.588235294x + x2 = 0.865916955

Factor a perfect square on the left side:
(x + 1.794117647)(x + 1.794117647) = 0.865916955

Calculate the square root of the right side: 0.930546589

Break this problem into two subproblems by setting 
(x + 1.794117647) equal to 0.930546589 and -0.930546589.

Subproblem 1

x + 1.794117647 = 0.930546589 Simplifying x + 1.794117647 = 0.930546589 Reorder the terms: 1.794117647 + x = 0.930546589 Solving 1.794117647 + x = 0.930546589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.794117647' to each side of the equation. 1.794117647 + -1.794117647 + x = 0.930546589 + -1.794117647 Combine like terms: 1.794117647 + -1.794117647 = 0.000000000 0.000000000 + x = 0.930546589 + -1.794117647 x = 0.930546589 + -1.794117647 Combine like terms: 0.930546589 + -1.794117647 = -0.863571058 x = -0.863571058 Simplifying x = -0.863571058

Subproblem 2

x + 1.794117647 = -0.930546589 Simplifying x + 1.794117647 = -0.930546589 Reorder the terms: 1.794117647 + x = -0.930546589 Solving 1.794117647 + x = -0.930546589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.794117647' to each side of the equation. 1.794117647 + -1.794117647 + x = -0.930546589 + -1.794117647 Combine like terms: 1.794117647 + -1.794117647 = 0.000000000 0.000000000 + x = -0.930546589 + -1.794117647 x = -0.930546589 + -1.794117647 Combine like terms: -0.930546589 + -1.794117647 = -2.724664236 x = -2.724664236 Simplifying x = -2.724664236

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.863571058, -2.724664236}

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