(3x-2)(x-5)=17

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Solution for (3x-2)(x-5)=17 equation:


Simplifying
(3x + -2)(x + -5) = 17

Reorder the terms:
(-2 + 3x)(x + -5) = 17

Reorder the terms:
(-2 + 3x)(-5 + x) = 17

Multiply (-2 + 3x) * (-5 + x)
(-2(-5 + x) + 3x * (-5 + x)) = 17
((-5 * -2 + x * -2) + 3x * (-5 + x)) = 17
((10 + -2x) + 3x * (-5 + x)) = 17
(10 + -2x + (-5 * 3x + x * 3x)) = 17
(10 + -2x + (-15x + 3x2)) = 17

Combine like terms: -2x + -15x = -17x
(10 + -17x + 3x2) = 17

Solving
10 + -17x + 3x2 = 17

Solving for variable 'x'.

Reorder the terms:
10 + -17 + -17x + 3x2 = 17 + -17

Combine like terms: 10 + -17 = -7
-7 + -17x + 3x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-7 + -17x + 3x2 = 0

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

Divide each side by '3'.
-2.333333333 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -5.666666667x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -5.666666667x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -5.666666667x + x2 = 0 + 2.333333333
-5.666666667x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-5.666666667x + x2 = 2.333333333

The x term is -5.666666667x.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667x + 8.027777782 + x2 = 2.333333333 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = 2.333333333 + 8.027777782

Combine like terms: 2.333333333 + 8.027777782 = 10.361111115
8.027777782 + -5.666666667x + x2 = 10.361111115

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 10.361111115

Calculate the square root of the right side: 3.218867987

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 3.218867987 and -3.218867987.

Subproblem 1

x + -2.833333334 = 3.218867987 Simplifying x + -2.833333334 = 3.218867987 Reorder the terms: -2.833333334 + x = 3.218867987 Solving -2.833333334 + x = 3.218867987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 3.218867987 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 3.218867987 + 2.833333334 x = 3.218867987 + 2.833333334 Combine like terms: 3.218867987 + 2.833333334 = 6.052201321 x = 6.052201321 Simplifying x = 6.052201321

Subproblem 2

x + -2.833333334 = -3.218867987 Simplifying x + -2.833333334 = -3.218867987 Reorder the terms: -2.833333334 + x = -3.218867987 Solving -2.833333334 + x = -3.218867987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -3.218867987 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -3.218867987 + 2.833333334 x = -3.218867987 + 2.833333334 Combine like terms: -3.218867987 + 2.833333334 = -0.385534653 x = -0.385534653 Simplifying x = -0.385534653

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.052201321, -0.385534653}

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