(2x^2+3x-9)-(2x+5)=

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Solution for (2x^2+3x-9)-(2x+5)= equation:


Simplifying
(2x2 + 3x + -9) + -1(2x + 5) = 0

Reorder the terms:
(-9 + 3x + 2x2) + -1(2x + 5) = 0

Remove parenthesis around (-9 + 3x + 2x2)
-9 + 3x + 2x2 + -1(2x + 5) = 0

Reorder the terms:
-9 + 3x + 2x2 + -1(5 + 2x) = 0
-9 + 3x + 2x2 + (5 * -1 + 2x * -1) = 0
-9 + 3x + 2x2 + (-5 + -2x) = 0

Reorder the terms:
-9 + -5 + 3x + -2x + 2x2 = 0

Combine like terms: -9 + -5 = -14
-14 + 3x + -2x + 2x2 = 0

Combine like terms: 3x + -2x = 1x
-14 + 1x + 2x2 = 0

Solving
-14 + 1x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-7 + 0.5x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 0.5x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 0.5x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 0.5x + x2 = 0 + 7
0.5x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
0.5x + x2 = 7

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 7 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 7 + 0.0625

Combine like terms: 7 + 0.0625 = 7.0625
0.0625 + 0.5x + x2 = 7.0625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(x + 0.25) equal to 2.657536453 and -2.657536453.

Subproblem 1

x + 0.25 = 2.657536453 Simplifying x + 0.25 = 2.657536453 Reorder the terms: 0.25 + x = 2.657536453 Solving 0.25 + x = 2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.657536453 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.657536453 + -0.25 x = 2.657536453 + -0.25 Combine like terms: 2.657536453 + -0.25 = 2.407536453 x = 2.407536453 Simplifying x = 2.407536453

Subproblem 2

x + 0.25 = -2.657536453 Simplifying x + 0.25 = -2.657536453 Reorder the terms: 0.25 + x = -2.657536453 Solving 0.25 + x = -2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.657536453 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.657536453 + -0.25 x = -2.657536453 + -0.25 Combine like terms: -2.657536453 + -0.25 = -2.907536453 x = -2.907536453 Simplifying x = -2.907536453

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.407536453, -2.907536453}

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