2x^2+5x-14=20

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Solution for 2x^2+5x-14=20 equation:


Simplifying
2x2 + 5x + -14 = 20

Reorder the terms:
-14 + 5x + 2x2 = 20

Solving
-14 + 5x + 2x2 = 20

Solving for variable 'x'.

Reorder the terms:
-14 + -20 + 5x + 2x2 = 20 + -20

Combine like terms: -14 + -20 = -34
-34 + 5x + 2x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-34 + 5x + 2x2 = 0

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

Divide each side by '2'.
-17 + 2.5x + x2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 2.5x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 2.5x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 2.5x + x2 = 0 + 17
2.5x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
2.5x + x2 = 17

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 17 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 17 + 1.5625

Combine like terms: 17 + 1.5625 = 18.5625
1.5625 + 2.5x + x2 = 18.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 18.5625

Calculate the square root of the right side: 4.308421985

Break this problem into two subproblems by setting 
(x + 1.25) equal to 4.308421985 and -4.308421985.

Subproblem 1

x + 1.25 = 4.308421985 Simplifying x + 1.25 = 4.308421985 Reorder the terms: 1.25 + x = 4.308421985 Solving 1.25 + x = 4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 4.308421985 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 4.308421985 + -1.25 x = 4.308421985 + -1.25 Combine like terms: 4.308421985 + -1.25 = 3.058421985 x = 3.058421985 Simplifying x = 3.058421985

Subproblem 2

x + 1.25 = -4.308421985 Simplifying x + 1.25 = -4.308421985 Reorder the terms: 1.25 + x = -4.308421985 Solving 1.25 + x = -4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -4.308421985 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -4.308421985 + -1.25 x = -4.308421985 + -1.25 Combine like terms: -4.308421985 + -1.25 = -5.558421985 x = -5.558421985 Simplifying x = -5.558421985

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.058421985, -5.558421985}

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