17x^2+27x+7=0

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Solution for 17x^2+27x+7=0 equation:


Simplifying
17x2 + 27x + 7 = 0

Reorder the terms:
7 + 27x + 17x2 = 0

Solving
7 + 27x + 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'.
0.4117647059 + 1.588235294x + x2 = 0

Move the constant term to the right:

Add '-0.4117647059' to each side of the equation.
0.4117647059 + 1.588235294x + -0.4117647059 + x2 = 0 + -0.4117647059

Reorder the terms:
0.4117647059 + -0.4117647059 + 1.588235294x + x2 = 0 + -0.4117647059

Combine like terms: 0.4117647059 + -0.4117647059 = 0.0000000000
0.0000000000 + 1.588235294x + x2 = 0 + -0.4117647059
1.588235294x + x2 = 0 + -0.4117647059

Combine like terms: 0 + -0.4117647059 = -0.4117647059
1.588235294x + x2 = -0.4117647059

The x term is 1.588235294x.  Take half its coefficient (0.794117647).
Square it (0.6306228373) and add it to both sides.

Add '0.6306228373' to each side of the equation.
1.588235294x + 0.6306228373 + x2 = -0.4117647059 + 0.6306228373

Reorder the terms:
0.6306228373 + 1.588235294x + x2 = -0.4117647059 + 0.6306228373

Combine like terms: -0.4117647059 + 0.6306228373 = 0.2188581314
0.6306228373 + 1.588235294x + x2 = 0.2188581314

Factor a perfect square on the left side:
(x + 0.794117647)(x + 0.794117647) = 0.2188581314

Calculate the square root of the right side: 0.467822756

Break this problem into two subproblems by setting 
(x + 0.794117647) equal to 0.467822756 and -0.467822756.

Subproblem 1

x + 0.794117647 = 0.467822756 Simplifying x + 0.794117647 = 0.467822756 Reorder the terms: 0.794117647 + x = 0.467822756 Solving 0.794117647 + x = 0.467822756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.794117647' to each side of the equation. 0.794117647 + -0.794117647 + x = 0.467822756 + -0.794117647 Combine like terms: 0.794117647 + -0.794117647 = 0.000000000 0.000000000 + x = 0.467822756 + -0.794117647 x = 0.467822756 + -0.794117647 Combine like terms: 0.467822756 + -0.794117647 = -0.326294891 x = -0.326294891 Simplifying x = -0.326294891

Subproblem 2

x + 0.794117647 = -0.467822756 Simplifying x + 0.794117647 = -0.467822756 Reorder the terms: 0.794117647 + x = -0.467822756 Solving 0.794117647 + x = -0.467822756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.794117647' to each side of the equation. 0.794117647 + -0.794117647 + x = -0.467822756 + -0.794117647 Combine like terms: 0.794117647 + -0.794117647 = 0.000000000 0.000000000 + x = -0.467822756 + -0.794117647 x = -0.467822756 + -0.794117647 Combine like terms: -0.467822756 + -0.794117647 = -1.261940403 x = -1.261940403 Simplifying x = -1.261940403

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.326294891, -1.261940403}

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