x^2-8+24x=30x+10

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Solution for x^2-8+24x=30x+10 equation:


Simplifying
x2 + -8 + 24x = 30x + 10

Reorder the terms:
-8 + 24x + x2 = 30x + 10

Reorder the terms:
-8 + 24x + x2 = 10 + 30x

Solving
-8 + 24x + x2 = 10 + 30x

Solving for variable 'x'.

Reorder the terms:
-8 + -10 + 24x + -30x + x2 = 10 + 30x + -10 + -30x

Combine like terms: -8 + -10 = -18
-18 + 24x + -30x + x2 = 10 + 30x + -10 + -30x

Combine like terms: 24x + -30x = -6x
-18 + -6x + x2 = 10 + 30x + -10 + -30x

Reorder the terms:
-18 + -6x + x2 = 10 + -10 + 30x + -30x

Combine like terms: 10 + -10 = 0
-18 + -6x + x2 = 0 + 30x + -30x
-18 + -6x + x2 = 30x + -30x

Combine like terms: 30x + -30x = 0
-18 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -6x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -6x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -6x + x2 = 0 + 18
-6x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-6x + x2 = 18

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 18 + 9

Reorder the terms:
9 + -6x + x2 = 18 + 9

Combine like terms: 18 + 9 = 27
9 + -6x + x2 = 27

Factor a perfect square on the left side:
(x + -3)(x + -3) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + -3) equal to 5.196152423 and -5.196152423.

Subproblem 1

x + -3 = 5.196152423 Simplifying x + -3 = 5.196152423 Reorder the terms: -3 + x = 5.196152423 Solving -3 + x = 5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.196152423 + 3 x = 5.196152423 + 3 Combine like terms: 5.196152423 + 3 = 8.196152423 x = 8.196152423 Simplifying x = 8.196152423

Subproblem 2

x + -3 = -5.196152423 Simplifying x + -3 = -5.196152423 Reorder the terms: -3 + x = -5.196152423 Solving -3 + x = -5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.196152423 + 3 x = -5.196152423 + 3 Combine like terms: -5.196152423 + 3 = -2.196152423 x = -2.196152423 Simplifying x = -2.196152423

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.196152423, -2.196152423}

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