2x^2+14x-22.5=0

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Solution for 2x^2+14x-22.5=0 equation:


Simplifying
2x2 + 14x + -22.5 = 0

Reorder the terms:
-22.5 + 14x + 2x2 = 0

Solving
-22.5 + 14x + 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'.
-11.25 + 7x + x2 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + 7x + 11.25 + x2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + 7x + x2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + 7x + x2 = 0 + 11.25
7x + x2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
7x + x2 = 11.25

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 11.25 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 11.25 + 12.25

Combine like terms: 11.25 + 12.25 = 23.5
12.25 + 7x + x2 = 23.5

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 23.5

Calculate the square root of the right side: 4.847679857

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.847679857 and -4.847679857.

Subproblem 1

x + 3.5 = 4.847679857 Simplifying x + 3.5 = 4.847679857 Reorder the terms: 3.5 + x = 4.847679857 Solving 3.5 + x = 4.847679857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.847679857 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.847679857 + -3.5 x = 4.847679857 + -3.5 Combine like terms: 4.847679857 + -3.5 = 1.347679857 x = 1.347679857 Simplifying x = 1.347679857

Subproblem 2

x + 3.5 = -4.847679857 Simplifying x + 3.5 = -4.847679857 Reorder the terms: 3.5 + x = -4.847679857 Solving 3.5 + x = -4.847679857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.847679857 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.847679857 + -3.5 x = -4.847679857 + -3.5 Combine like terms: -4.847679857 + -3.5 = -8.347679857 x = -8.347679857 Simplifying x = -8.347679857

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.347679857, -8.347679857}

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