x*x+10=6*3x

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Solution for x*x+10=6*3x equation:


Simplifying
x * x + 10 = 6 * 3x

Multiply x * x
x2 + 10 = 6 * 3x

Reorder the terms:
10 + x2 = 6 * 3x

Multiply 6 * 3
10 + x2 = 18x

Solving
10 + x2 = 18x

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -18x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -18x + x2 = 0 + -10

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

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

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -10 + 81

Reorder the terms:
81 + -18x + x2 = -10 + 81

Combine like terms: -10 + 81 = 71
81 + -18x + x2 = 71

Factor a perfect square on the left side:
(x + -9)(x + -9) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + -9) equal to 8.426149773 and -8.426149773.

Subproblem 1

x + -9 = 8.426149773 Simplifying x + -9 = 8.426149773 Reorder the terms: -9 + x = 8.426149773 Solving -9 + x = 8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 8.426149773 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.426149773 + 9 x = 8.426149773 + 9 Combine like terms: 8.426149773 + 9 = 17.426149773 x = 17.426149773 Simplifying x = 17.426149773

Subproblem 2

x + -9 = -8.426149773 Simplifying x + -9 = -8.426149773 Reorder the terms: -9 + x = -8.426149773 Solving -9 + x = -8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -8.426149773 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.426149773 + 9 x = -8.426149773 + 9 Combine like terms: -8.426149773 + 9 = 0.573850227 x = 0.573850227 Simplifying x = 0.573850227

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.426149773, 0.573850227}

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