1x(3x-10)=90

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Solution for 1x(3x-10)=90 equation:


Simplifying
1x(3x + -10) = 90

Reorder the terms:
1x(-10 + 3x) = 90
(-10 * 1x + 3x * 1x) = 90
(-10x + 3x2) = 90

Solving
-10x + 3x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + -10x + 3x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -10x + 3x2 = 0

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

Divide each side by '3'.
-30 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -3.333333333x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -3.333333333x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -3.333333333x + x2 = 0 + 30
-3.333333333x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-3.333333333x + x2 = 30

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 30 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 30 + 2.777777779

Combine like terms: 30 + 2.777777779 = 32.777777779
2.777777779 + -3.333333333x + x2 = 32.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 32.777777779

Calculate the square root of the right side: 5.725188013

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 5.725188013 and -5.725188013.

Subproblem 1

x + -1.666666667 = 5.725188013 Simplifying x + -1.666666667 = 5.725188013 Reorder the terms: -1.666666667 + x = 5.725188013 Solving -1.666666667 + x = 5.725188013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 5.725188013 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 5.725188013 + 1.666666667 x = 5.725188013 + 1.666666667 Combine like terms: 5.725188013 + 1.666666667 = 7.39185468 x = 7.39185468 Simplifying x = 7.39185468

Subproblem 2

x + -1.666666667 = -5.725188013 Simplifying x + -1.666666667 = -5.725188013 Reorder the terms: -1.666666667 + x = -5.725188013 Solving -1.666666667 + x = -5.725188013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -5.725188013 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -5.725188013 + 1.666666667 x = -5.725188013 + 1.666666667 Combine like terms: -5.725188013 + 1.666666667 = -4.058521346 x = -4.058521346 Simplifying x = -4.058521346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.39185468, -4.058521346}

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