-2x^2-9x+14=0

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Solution for -2x^2-9x+14=0 equation:


Simplifying
-2x2 + -9x + 14 = 0

Reorder the terms:
14 + -9x + -2x2 = 0

Solving
14 + -9x + -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 + 4.5x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 4.5x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 4.5x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 4.5x + x2 = 0 + 7
4.5x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
4.5x + x2 = 7

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 = 7 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 7 + 5.0625

Combine like terms: 7 + 5.0625 = 12.0625
5.0625 + 4.5x + x2 = 12.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 12.0625

Calculate the square root of the right side: 3.473110997

Break this problem into two subproblems by setting 
(x + 2.25) equal to 3.473110997 and -3.473110997.

Subproblem 1

x + 2.25 = 3.473110997 Simplifying x + 2.25 = 3.473110997 Reorder the terms: 2.25 + x = 3.473110997 Solving 2.25 + x = 3.473110997 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 = 3.473110997 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.473110997 + -2.25 x = 3.473110997 + -2.25 Combine like terms: 3.473110997 + -2.25 = 1.223110997 x = 1.223110997 Simplifying x = 1.223110997

Subproblem 2

x + 2.25 = -3.473110997 Simplifying x + 2.25 = -3.473110997 Reorder the terms: 2.25 + x = -3.473110997 Solving 2.25 + x = -3.473110997 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 = -3.473110997 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.473110997 + -2.25 x = -3.473110997 + -2.25 Combine like terms: -3.473110997 + -2.25 = -5.723110997 x = -5.723110997 Simplifying x = -5.723110997

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.223110997, -5.723110997}

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