2x^2+7x=-4

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Solution for 2x^2+7x=-4 equation:


Simplifying
2x2 + 7x = -4

Reorder the terms:
7x + 2x2 = -4

Solving
7x + 2x2 = -4

Solving for variable 'x'.

Reorder the terms:
4 + 7x + 2x2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 7x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
2 + 3.5x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 3.5x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 3.5x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3.5x + x2 = 0 + -2
3.5x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
3.5x + x2 = -2

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 = -2 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = -2 + 3.0625

Combine like terms: -2 + 3.0625 = 1.0625
3.0625 + 3.5x + x2 = 1.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(x + 1.75) equal to 1.030776406 and -1.030776406.

Subproblem 1

x + 1.75 = 1.030776406 Simplifying x + 1.75 = 1.030776406 Reorder the terms: 1.75 + x = 1.030776406 Solving 1.75 + x = 1.030776406 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 = 1.030776406 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 1.030776406 + -1.75 x = 1.030776406 + -1.75 Combine like terms: 1.030776406 + -1.75 = -0.719223594 x = -0.719223594 Simplifying x = -0.719223594

Subproblem 2

x + 1.75 = -1.030776406 Simplifying x + 1.75 = -1.030776406 Reorder the terms: 1.75 + x = -1.030776406 Solving 1.75 + x = -1.030776406 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 = -1.030776406 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -1.030776406 + -1.75 x = -1.030776406 + -1.75 Combine like terms: -1.030776406 + -1.75 = -2.780776406 x = -2.780776406 Simplifying x = -2.780776406

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.719223594, -2.780776406}

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