7x-3x(x-6)=30

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Solution for 7x-3x(x-6)=30 equation:


Simplifying
7x + -3x(x + -6) = 30

Reorder the terms:
7x + -3x(-6 + x) = 30
7x + (-6 * -3x + x * -3x) = 30
7x + (18x + -3x2) = 30

Combine like terms: 7x + 18x = 25x
25x + -3x2 = 30

Solving
25x + -3x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + 25x + -3x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 25x + -3x2 = 0

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

Divide each side by '-3'.
10 + -8.333333333x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -8.333333333x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -8.333333333x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -8.333333333x + x2 = 0 + -10
-8.333333333x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-8.333333333x + x2 = -10

The x term is -8.333333333x.  Take half its coefficient (-4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
-8.333333333x + 17.36111111 + x2 = -10 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333x + x2 = -10 + 17.36111111

Combine like terms: -10 + 17.36111111 = 7.36111111
17.36111111 + -8.333333333x + x2 = 7.36111111

Factor a perfect square on the left side:
(x + -4.166666667)(x + -4.166666667) = 7.36111111

Calculate the square root of the right side: 2.713136766

Break this problem into two subproblems by setting 
(x + -4.166666667) equal to 2.713136766 and -2.713136766.

Subproblem 1

x + -4.166666667 = 2.713136766 Simplifying x + -4.166666667 = 2.713136766 Reorder the terms: -4.166666667 + x = 2.713136766 Solving -4.166666667 + x = 2.713136766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = 2.713136766 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = 2.713136766 + 4.166666667 x = 2.713136766 + 4.166666667 Combine like terms: 2.713136766 + 4.166666667 = 6.879803433 x = 6.879803433 Simplifying x = 6.879803433

Subproblem 2

x + -4.166666667 = -2.713136766 Simplifying x + -4.166666667 = -2.713136766 Reorder the terms: -4.166666667 + x = -2.713136766 Solving -4.166666667 + x = -2.713136766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = -2.713136766 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = -2.713136766 + 4.166666667 x = -2.713136766 + 4.166666667 Combine like terms: -2.713136766 + 4.166666667 = 1.453529901 x = 1.453529901 Simplifying x = 1.453529901

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.879803433, 1.453529901}

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