x^2-18x=-3

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Solution for x^2-18x=-3 equation:


Simplifying
x2 + -18x = -3

Reorder the terms:
-18x + x2 = -3

Solving
-18x + x2 = -3

Solving for variable 'x'.

Reorder the terms:
3 + -18x + x2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + -18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -18x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -18x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -18x + x2 = 0 + -3
-18x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-18x + x2 = -3

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 = -3 + 81

Reorder the terms:
81 + -18x + x2 = -3 + 81

Combine like terms: -3 + 81 = 78
81 + -18x + x2 = 78

Factor a perfect square on the left side:
(x + -9)(x + -9) = 78

Calculate the square root of the right side: 8.831760866

Break this problem into two subproblems by setting 
(x + -9) equal to 8.831760866 and -8.831760866.

Subproblem 1

x + -9 = 8.831760866 Simplifying x + -9 = 8.831760866 Reorder the terms: -9 + x = 8.831760866 Solving -9 + x = 8.831760866 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 = 8.831760866 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.831760866 + 9 x = 8.831760866 + 9 Combine like terms: 8.831760866 + 9 = 17.831760866 x = 17.831760866 Simplifying x = 17.831760866

Subproblem 2

x + -9 = -8.831760866 Simplifying x + -9 = -8.831760866 Reorder the terms: -9 + x = -8.831760866 Solving -9 + x = -8.831760866 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 = -8.831760866 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.831760866 + 9 x = -8.831760866 + 9 Combine like terms: -8.831760866 + 9 = 0.168239134 x = 0.168239134 Simplifying x = 0.168239134

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.831760866, 0.168239134}

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