x^2-6x=10(1-3x)

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Solution for x^2-6x=10(1-3x) equation:


Simplifying
x2 + -6x = 10(1 + -3x)

Reorder the terms:
-6x + x2 = 10(1 + -3x)
-6x + x2 = (1 * 10 + -3x * 10)
-6x + x2 = (10 + -30x)

Solving
-6x + x2 = 10 + -30x

Solving for variable 'x'.

Reorder the terms:
-10 + -6x + 30x + x2 = 10 + -30x + -10 + 30x

Combine like terms: -6x + 30x = 24x
-10 + 24x + x2 = 10 + -30x + -10 + 30x

Reorder the terms:
-10 + 24x + x2 = 10 + -10 + -30x + 30x

Combine like terms: 10 + -10 = 0
-10 + 24x + x2 = 0 + -30x + 30x
-10 + 24x + x2 = -30x + 30x

Combine like terms: -30x + 30x = 0
-10 + 24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 24x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 24x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 24x + x2 = 0 + 10
24x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
24x + x2 = 10

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = 10 + 144

Reorder the terms:
144 + 24x + x2 = 10 + 144

Combine like terms: 10 + 144 = 154
144 + 24x + x2 = 154

Factor a perfect square on the left side:
(x + 12)(x + 12) = 154

Calculate the square root of the right side: 12.409673646

Break this problem into two subproblems by setting 
(x + 12) equal to 12.409673646 and -12.409673646.

Subproblem 1

x + 12 = 12.409673646 Simplifying x + 12 = 12.409673646 Reorder the terms: 12 + x = 12.409673646 Solving 12 + x = 12.409673646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 12.409673646 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.409673646 + -12 x = 12.409673646 + -12 Combine like terms: 12.409673646 + -12 = 0.409673646 x = 0.409673646 Simplifying x = 0.409673646

Subproblem 2

x + 12 = -12.409673646 Simplifying x + 12 = -12.409673646 Reorder the terms: 12 + x = -12.409673646 Solving 12 + x = -12.409673646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -12.409673646 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.409673646 + -12 x = -12.409673646 + -12 Combine like terms: -12.409673646 + -12 = -24.409673646 x = -24.409673646 Simplifying x = -24.409673646

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.409673646, -24.409673646}

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