(4x^2-7x-17)+(2x^2+9x)=

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Solution for (4x^2-7x-17)+(2x^2+9x)= equation:


Simplifying
(4x2 + -7x + -17) + (2x2 + 9x) = 0

Reorder the terms:
(-17 + -7x + 4x2) + (2x2 + 9x) = 0

Remove parenthesis around (-17 + -7x + 4x2)
-17 + -7x + 4x2 + (2x2 + 9x) = 0

Reorder the terms:
-17 + -7x + 4x2 + (9x + 2x2) = 0

Remove parenthesis around (9x + 2x2)
-17 + -7x + 4x2 + 9x + 2x2 = 0

Reorder the terms:
-17 + -7x + 9x + 4x2 + 2x2 = 0

Combine like terms: -7x + 9x = 2x
-17 + 2x + 4x2 + 2x2 = 0

Combine like terms: 4x2 + 2x2 = 6x2
-17 + 2x + 6x2 = 0

Solving
-17 + 2x + 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'.
-2.833333333 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + 0.3333333333x + 2.833333333 + x2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + 0.3333333333x + x2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + 0.3333333333x + x2 = 0 + 2.833333333
0.3333333333x + x2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
0.3333333333x + x2 = 2.833333333

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 2.833333333 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 2.833333333 + 0.02777777779

Combine like terms: 2.833333333 + 0.02777777779 = 2.86111111079
0.02777777779 + 0.3333333333x + x2 = 2.86111111079

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 2.86111111079

Calculate the square root of the right side: 1.691481927

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 1.691481927 and -1.691481927.

Subproblem 1

x + 0.1666666667 = 1.691481927 Simplifying x + 0.1666666667 = 1.691481927 Reorder the terms: 0.1666666667 + x = 1.691481927 Solving 0.1666666667 + x = 1.691481927 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 1.691481927 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 1.691481927 + -0.1666666667 x = 1.691481927 + -0.1666666667 Combine like terms: 1.691481927 + -0.1666666667 = 1.5248152603 x = 1.5248152603 Simplifying x = 1.5248152603

Subproblem 2

x + 0.1666666667 = -1.691481927 Simplifying x + 0.1666666667 = -1.691481927 Reorder the terms: 0.1666666667 + x = -1.691481927 Solving 0.1666666667 + x = -1.691481927 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -1.691481927 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -1.691481927 + -0.1666666667 x = -1.691481927 + -0.1666666667 Combine like terms: -1.691481927 + -0.1666666667 = -1.8581485937 x = -1.8581485937 Simplifying x = -1.8581485937

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.5248152603, -1.8581485937}

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