2x^2+7x-83=0

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Solution for 2x^2+7x-83=0 equation:


Simplifying
2x2 + 7x + -83 = 0

Reorder the terms:
-83 + 7x + 2x2 = 0

Solving
-83 + 7x + 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'.
-41.5 + 3.5x + x2 = 0

Move the constant term to the right:

Add '41.5' to each side of the equation.
-41.5 + 3.5x + 41.5 + x2 = 0 + 41.5

Reorder the terms:
-41.5 + 41.5 + 3.5x + x2 = 0 + 41.5

Combine like terms: -41.5 + 41.5 = 0.0
0.0 + 3.5x + x2 = 0 + 41.5
3.5x + x2 = 0 + 41.5

Combine like terms: 0 + 41.5 = 41.5
3.5x + x2 = 41.5

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 41.5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 41.5 + 3.0625

Combine like terms: 41.5 + 3.0625 = 44.5625
3.0625 + 3.5x + x2 = 44.5625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 44.5625

Calculate the square root of the right side: 6.675514961

Break this problem into two subproblems by setting 
(x + 1.75) equal to 6.675514961 and -6.675514961.

Subproblem 1

x + 1.75 = 6.675514961 Simplifying x + 1.75 = 6.675514961 Reorder the terms: 1.75 + x = 6.675514961 Solving 1.75 + x = 6.675514961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 6.675514961 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 6.675514961 + -1.75 x = 6.675514961 + -1.75 Combine like terms: 6.675514961 + -1.75 = 4.925514961 x = 4.925514961 Simplifying x = 4.925514961

Subproblem 2

x + 1.75 = -6.675514961 Simplifying x + 1.75 = -6.675514961 Reorder the terms: 1.75 + x = -6.675514961 Solving 1.75 + x = -6.675514961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -6.675514961 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -6.675514961 + -1.75 x = -6.675514961 + -1.75 Combine like terms: -6.675514961 + -1.75 = -8.425514961 x = -8.425514961 Simplifying x = -8.425514961

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.925514961, -8.425514961}

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