2x^2+14x+21.5=0

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Solution for 2x^2+14x+21.5=0 equation:


Simplifying
2x2 + 14x + 21.5 = 0

Reorder the terms:
21.5 + 14x + 2x2 = 0

Solving
21.5 + 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'.
10.75 + 7x + x2 = 0

Move the constant term to the right:

Add '-10.75' to each side of the equation.
10.75 + 7x + -10.75 + x2 = 0 + -10.75

Reorder the terms:
10.75 + -10.75 + 7x + x2 = 0 + -10.75

Combine like terms: 10.75 + -10.75 = 0.00
0.00 + 7x + x2 = 0 + -10.75
7x + x2 = 0 + -10.75

Combine like terms: 0 + -10.75 = -10.75
7x + x2 = -10.75

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 = -10.75 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -10.75 + 12.25

Combine like terms: -10.75 + 12.25 = 1.5
12.25 + 7x + x2 = 1.5

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + 3.5) equal to 1.224744871 and -1.224744871.

Subproblem 1

x + 3.5 = 1.224744871 Simplifying x + 3.5 = 1.224744871 Reorder the terms: 3.5 + x = 1.224744871 Solving 3.5 + x = 1.224744871 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 = 1.224744871 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 1.224744871 + -3.5 x = 1.224744871 + -3.5 Combine like terms: 1.224744871 + -3.5 = -2.275255129 x = -2.275255129 Simplifying x = -2.275255129

Subproblem 2

x + 3.5 = -1.224744871 Simplifying x + 3.5 = -1.224744871 Reorder the terms: 3.5 + x = -1.224744871 Solving 3.5 + x = -1.224744871 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 = -1.224744871 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -1.224744871 + -3.5 x = -1.224744871 + -3.5 Combine like terms: -1.224744871 + -3.5 = -4.724744871 x = -4.724744871 Simplifying x = -4.724744871

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.275255129, -4.724744871}

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