2x^2=9x+40

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Solution for 2x^2=9x+40 equation:


Simplifying
2x2 = 9x + 40

Reorder the terms:
2x2 = 40 + 9x

Solving
2x2 = 40 + 9x

Solving for variable 'x'.

Reorder the terms:
-40 + -9x + 2x2 = 40 + 9x + -40 + -9x

Reorder the terms:
-40 + -9x + 2x2 = 40 + -40 + 9x + -9x

Combine like terms: 40 + -40 = 0
-40 + -9x + 2x2 = 0 + 9x + -9x
-40 + -9x + 2x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-40 + -9x + 2x2 = 0

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

Divide each side by '2'.
-20 + -4.5x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -4.5x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -4.5x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -4.5x + x2 = 0 + 20
-4.5x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-4.5x + x2 = 20

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 20 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 20 + 5.0625

Combine like terms: 20 + 5.0625 = 25.0625
5.0625 + -4.5x + x2 = 25.0625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 25.0625

Calculate the square root of the right side: 5.006246099

Break this problem into two subproblems by setting 
(x + -2.25) equal to 5.006246099 and -5.006246099.

Subproblem 1

x + -2.25 = 5.006246099 Simplifying x + -2.25 = 5.006246099 Reorder the terms: -2.25 + x = 5.006246099 Solving -2.25 + x = 5.006246099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 5.006246099 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 5.006246099 + 2.25 x = 5.006246099 + 2.25 Combine like terms: 5.006246099 + 2.25 = 7.256246099 x = 7.256246099 Simplifying x = 7.256246099

Subproblem 2

x + -2.25 = -5.006246099 Simplifying x + -2.25 = -5.006246099 Reorder the terms: -2.25 + x = -5.006246099 Solving -2.25 + x = -5.006246099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -5.006246099 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -5.006246099 + 2.25 x = -5.006246099 + 2.25 Combine like terms: -5.006246099 + 2.25 = -2.756246099 x = -2.756246099 Simplifying x = -2.756246099

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.256246099, -2.756246099}

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