2.25x^2-9x-9=18

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Solution for 2.25x^2-9x-9=18 equation:


Simplifying
2.25x2 + -9x + -9 = 18

Reorder the terms:
-9 + -9x + 2.25x2 = 18

Solving
-9 + -9x + 2.25x2 = 18

Solving for variable 'x'.

Reorder the terms:
-9 + -18 + -9x + 2.25x2 = 18 + -18

Combine like terms: -9 + -18 = -27
-27 + -9x + 2.25x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-27 + -9x + 2.25x2 = 0

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

Divide each side by '2.25'.
-12 + -4x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -4x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -4x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -4x + x2 = 0 + 12
-4x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-4x + x2 = 12

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 12 + 4

Reorder the terms:
4 + -4x + x2 = 12 + 4

Combine like terms: 12 + 4 = 16
4 + -4x + x2 = 16

Factor a perfect square on the left side:
(x + -2)(x + -2) = 16

Calculate the square root of the right side: 4

Break this problem into two subproblems by setting 
(x + -2) equal to 4 and -4.

Subproblem 1

x + -2 = 4 Simplifying x + -2 = 4 Reorder the terms: -2 + x = 4 Solving -2 + x = 4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4 + 2 x = 4 + 2 Combine like terms: 4 + 2 = 6 x = 6 Simplifying x = 6

Subproblem 2

x + -2 = -4 Simplifying x + -2 = -4 Reorder the terms: -2 + x = -4 Solving -2 + x = -4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4 + 2 x = -4 + 2 Combine like terms: -4 + 2 = -2 x = -2 Simplifying x = -2

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6, -2}

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