2x^2+7x+-3=0

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Solution for 2x^2+7x+-3=0 equation:


Simplifying
2x2 + 7x + -3 = 0

Reorder the terms:
-3 + 7x + 2x2 = 0

Solving
-3 + 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'.
-1.5 + 3.5x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 3.5x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 3.5x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 3.5x + x2 = 0 + 1.5
3.5x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
3.5x + x2 = 1.5

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 = 1.5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 1.5 + 3.0625

Combine like terms: 1.5 + 3.0625 = 4.5625
3.0625 + 3.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + 1.75) equal to 2.136000936 and -2.136000936.

Subproblem 1

x + 1.75 = 2.136000936 Simplifying x + 1.75 = 2.136000936 Reorder the terms: 1.75 + x = 2.136000936 Solving 1.75 + x = 2.136000936 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 = 2.136000936 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.136000936 + -1.75 x = 2.136000936 + -1.75 Combine like terms: 2.136000936 + -1.75 = 0.386000936 x = 0.386000936 Simplifying x = 0.386000936

Subproblem 2

x + 1.75 = -2.136000936 Simplifying x + 1.75 = -2.136000936 Reorder the terms: 1.75 + x = -2.136000936 Solving 1.75 + x = -2.136000936 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 = -2.136000936 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.136000936 + -1.75 x = -2.136000936 + -1.75 Combine like terms: -2.136000936 + -1.75 = -3.886000936 x = -3.886000936 Simplifying x = -3.886000936

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.386000936, -3.886000936}

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