0=-17x^2+144x+160

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Solution for 0=-17x^2+144x+160 equation:


Simplifying
0 = -17x2 + 144x + 160

Reorder the terms:
0 = 160 + 144x + -17x2

Solving
0 = 160 + 144x + -17x2

Solving for variable 'x'.

Combine like terms: 0 + -160 = -160
-160 + -144x + 17x2 = 160 + 144x + -17x2 + -160 + -144x + 17x2

Reorder the terms:
-160 + -144x + 17x2 = 160 + -160 + 144x + -144x + -17x2 + 17x2

Combine like terms: 160 + -160 = 0
-160 + -144x + 17x2 = 0 + 144x + -144x + -17x2 + 17x2
-160 + -144x + 17x2 = 144x + -144x + -17x2 + 17x2

Combine like terms: 144x + -144x = 0
-160 + -144x + 17x2 = 0 + -17x2 + 17x2
-160 + -144x + 17x2 = -17x2 + 17x2

Combine like terms: -17x2 + 17x2 = 0
-160 + -144x + 17x2 = 0

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

Divide each side by '17'.
-9.411764706 + -8.470588235x + x2 = 0

Move the constant term to the right:

Add '9.411764706' to each side of the equation.
-9.411764706 + -8.470588235x + 9.411764706 + x2 = 0 + 9.411764706

Reorder the terms:
-9.411764706 + 9.411764706 + -8.470588235x + x2 = 0 + 9.411764706

Combine like terms: -9.411764706 + 9.411764706 = 0.000000000
0.000000000 + -8.470588235x + x2 = 0 + 9.411764706
-8.470588235x + x2 = 0 + 9.411764706

Combine like terms: 0 + 9.411764706 = 9.411764706
-8.470588235x + x2 = 9.411764706

The x term is -8.470588235x.  Take half its coefficient (-4.235294118).
Square it (17.93771627) and add it to both sides.

Add '17.93771627' to each side of the equation.
-8.470588235x + 17.93771627 + x2 = 9.411764706 + 17.93771627

Reorder the terms:
17.93771627 + -8.470588235x + x2 = 9.411764706 + 17.93771627

Combine like terms: 9.411764706 + 17.93771627 = 27.349480976
17.93771627 + -8.470588235x + x2 = 27.349480976

Factor a perfect square on the left side:
(x + -4.235294118)(x + -4.235294118) = 27.349480976

Calculate the square root of the right side: 5.229673123

Break this problem into two subproblems by setting 
(x + -4.235294118) equal to 5.229673123 and -5.229673123.

Subproblem 1

x + -4.235294118 = 5.229673123 Simplifying x + -4.235294118 = 5.229673123 Reorder the terms: -4.235294118 + x = 5.229673123 Solving -4.235294118 + x = 5.229673123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.235294118' to each side of the equation. -4.235294118 + 4.235294118 + x = 5.229673123 + 4.235294118 Combine like terms: -4.235294118 + 4.235294118 = 0.000000000 0.000000000 + x = 5.229673123 + 4.235294118 x = 5.229673123 + 4.235294118 Combine like terms: 5.229673123 + 4.235294118 = 9.464967241 x = 9.464967241 Simplifying x = 9.464967241

Subproblem 2

x + -4.235294118 = -5.229673123 Simplifying x + -4.235294118 = -5.229673123 Reorder the terms: -4.235294118 + x = -5.229673123 Solving -4.235294118 + x = -5.229673123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.235294118' to each side of the equation. -4.235294118 + 4.235294118 + x = -5.229673123 + 4.235294118 Combine like terms: -4.235294118 + 4.235294118 = 0.000000000 0.000000000 + x = -5.229673123 + 4.235294118 x = -5.229673123 + 4.235294118 Combine like terms: -5.229673123 + 4.235294118 = -0.994379005 x = -0.994379005 Simplifying x = -0.994379005

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.464967241, -0.994379005}

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