3x^2-24x+17=0

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Solution for 3x^2-24x+17=0 equation:


Simplifying
3x2 + -24x + 17 = 0

Reorder the terms:
17 + -24x + 3x2 = 0

Solving
17 + -24x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
5.666666667 + -8x + x2 = 0

Move the constant term to the right:

Add '-5.666666667' to each side of the equation.
5.666666667 + -8x + -5.666666667 + x2 = 0 + -5.666666667

Reorder the terms:
5.666666667 + -5.666666667 + -8x + x2 = 0 + -5.666666667

Combine like terms: 5.666666667 + -5.666666667 = 0.000000000
0.000000000 + -8x + x2 = 0 + -5.666666667
-8x + x2 = 0 + -5.666666667

Combine like terms: 0 + -5.666666667 = -5.666666667
-8x + x2 = -5.666666667

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -5.666666667 + 16

Reorder the terms:
16 + -8x + x2 = -5.666666667 + 16

Combine like terms: -5.666666667 + 16 = 10.333333333
16 + -8x + x2 = 10.333333333

Factor a perfect square on the left side:
(x + -4)(x + -4) = 10.333333333

Calculate the square root of the right side: 3.214550254

Break this problem into two subproblems by setting 
(x + -4) equal to 3.214550254 and -3.214550254.

Subproblem 1

x + -4 = 3.214550254 Simplifying x + -4 = 3.214550254 Reorder the terms: -4 + x = 3.214550254 Solving -4 + x = 3.214550254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.214550254 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.214550254 + 4 x = 3.214550254 + 4 Combine like terms: 3.214550254 + 4 = 7.214550254 x = 7.214550254 Simplifying x = 7.214550254

Subproblem 2

x + -4 = -3.214550254 Simplifying x + -4 = -3.214550254 Reorder the terms: -4 + x = -3.214550254 Solving -4 + x = -3.214550254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.214550254 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.214550254 + 4 x = -3.214550254 + 4 Combine like terms: -3.214550254 + 4 = 0.785449746 x = 0.785449746 Simplifying x = 0.785449746

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.214550254, 0.785449746}

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