9x^2-17x-7=0

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Solution for 9x^2-17x-7=0 equation:


Simplifying
9x2 + -17x + -7 = 0

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

Solving
-7 + -17x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-0.7777777778 + -1.888888889x + x2 = 0

Move the constant term to the right:

Add '0.7777777778' to each side of the equation.
-0.7777777778 + -1.888888889x + 0.7777777778 + x2 = 0 + 0.7777777778

Reorder the terms:
-0.7777777778 + 0.7777777778 + -1.888888889x + x2 = 0 + 0.7777777778

Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000
0.0000000000 + -1.888888889x + x2 = 0 + 0.7777777778
-1.888888889x + x2 = 0 + 0.7777777778

Combine like terms: 0 + 0.7777777778 = 0.7777777778
-1.888888889x + x2 = 0.7777777778

The x term is -1.888888889x.  Take half its coefficient (-0.9444444445).
Square it (0.8919753087) and add it to both sides.

Add '0.8919753087' to each side of the equation.
-1.888888889x + 0.8919753087 + x2 = 0.7777777778 + 0.8919753087

Reorder the terms:
0.8919753087 + -1.888888889x + x2 = 0.7777777778 + 0.8919753087

Combine like terms: 0.7777777778 + 0.8919753087 = 1.6697530865
0.8919753087 + -1.888888889x + x2 = 1.6697530865

Factor a perfect square on the left side:
(x + -0.9444444445)(x + -0.9444444445) = 1.6697530865

Calculate the square root of the right side: 1.292189261

Break this problem into two subproblems by setting 
(x + -0.9444444445) equal to 1.292189261 and -1.292189261.

Subproblem 1

x + -0.9444444445 = 1.292189261 Simplifying x + -0.9444444445 = 1.292189261 Reorder the terms: -0.9444444445 + x = 1.292189261 Solving -0.9444444445 + x = 1.292189261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = 1.292189261 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = 1.292189261 + 0.9444444445 x = 1.292189261 + 0.9444444445 Combine like terms: 1.292189261 + 0.9444444445 = 2.2366337055 x = 2.2366337055 Simplifying x = 2.2366337055

Subproblem 2

x + -0.9444444445 = -1.292189261 Simplifying x + -0.9444444445 = -1.292189261 Reorder the terms: -0.9444444445 + x = -1.292189261 Solving -0.9444444445 + x = -1.292189261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = -1.292189261 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = -1.292189261 + 0.9444444445 x = -1.292189261 + 0.9444444445 Combine like terms: -1.292189261 + 0.9444444445 = -0.3477448165 x = -0.3477448165 Simplifying x = -0.3477448165

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.2366337055, -0.3477448165}

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