6x^2+17x-4=

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Solution for 6x^2+17x-4= equation:


Simplifying
6x2 + 17x + -4 = 0

Reorder the terms:
-4 + 17x + 6x2 = 0

Solving
-4 + 17x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-0.6666666667 + 2.833333333x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 2.833333333x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 2.833333333x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 2.833333333x + x2 = 0 + 0.6666666667
2.833333333x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
2.833333333x + x2 = 0.6666666667

The x term is 2.833333333x.  Take half its coefficient (1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
2.833333333x + 2.006944445 + x2 = 0.6666666667 + 2.006944445

Reorder the terms:
2.006944445 + 2.833333333x + x2 = 0.6666666667 + 2.006944445

Combine like terms: 0.6666666667 + 2.006944445 = 2.6736111117
2.006944445 + 2.833333333x + x2 = 2.6736111117

Factor a perfect square on the left side:
(x + 1.416666667)(x + 1.416666667) = 2.6736111117

Calculate the square root of the right side: 1.635118073

Break this problem into two subproblems by setting 
(x + 1.416666667) equal to 1.635118073 and -1.635118073.

Subproblem 1

x + 1.416666667 = 1.635118073 Simplifying x + 1.416666667 = 1.635118073 Reorder the terms: 1.416666667 + x = 1.635118073 Solving 1.416666667 + x = 1.635118073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x = 1.635118073 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x = 1.635118073 + -1.416666667 x = 1.635118073 + -1.416666667 Combine like terms: 1.635118073 + -1.416666667 = 0.218451406 x = 0.218451406 Simplifying x = 0.218451406

Subproblem 2

x + 1.416666667 = -1.635118073 Simplifying x + 1.416666667 = -1.635118073 Reorder the terms: 1.416666667 + x = -1.635118073 Solving 1.416666667 + x = -1.635118073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x = -1.635118073 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x = -1.635118073 + -1.416666667 x = -1.635118073 + -1.416666667 Combine like terms: -1.635118073 + -1.416666667 = -3.05178474 x = -3.05178474 Simplifying x = -3.05178474

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.218451406, -3.05178474}

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