2x^2+7x-42=0

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Solution for 2x^2+7x-42=0 equation:


Simplifying
2x2 + 7x + -42 = 0

Reorder the terms:
-42 + 7x + 2x2 = 0

Solving
-42 + 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'.
-21 + 3.5x + x2 = 0

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 3.5x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 3.5x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 3.5x + x2 = 0 + 21
3.5x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
3.5x + x2 = 21

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 = 21 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 21 + 3.0625

Combine like terms: 21 + 3.0625 = 24.0625
3.0625 + 3.5x + x2 = 24.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 24.0625

Calculate the square root of the right side: 4.905354218

Break this problem into two subproblems by setting 
(x + 1.75) equal to 4.905354218 and -4.905354218.

Subproblem 1

x + 1.75 = 4.905354218 Simplifying x + 1.75 = 4.905354218 Reorder the terms: 1.75 + x = 4.905354218 Solving 1.75 + x = 4.905354218 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 = 4.905354218 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 4.905354218 + -1.75 x = 4.905354218 + -1.75 Combine like terms: 4.905354218 + -1.75 = 3.155354218 x = 3.155354218 Simplifying x = 3.155354218

Subproblem 2

x + 1.75 = -4.905354218 Simplifying x + 1.75 = -4.905354218 Reorder the terms: 1.75 + x = -4.905354218 Solving 1.75 + x = -4.905354218 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 = -4.905354218 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -4.905354218 + -1.75 x = -4.905354218 + -1.75 Combine like terms: -4.905354218 + -1.75 = -6.655354218 x = -6.655354218 Simplifying x = -6.655354218

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.155354218, -6.655354218}

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