2x^2+5x=56

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Solution for 2x^2+5x=56 equation:


Simplifying
2x2 + 5x = 56

Reorder the terms:
5x + 2x2 = 56

Solving
5x + 2x2 = 56

Solving for variable 'x'.

Reorder the terms:
-56 + 5x + 2x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-56 + 5x + 2x2 = 0

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

Divide each side by '2'.
-28 + 2.5x + x2 = 0

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 2.5x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 2.5x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 2.5x + x2 = 0 + 28
2.5x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
2.5x + x2 = 28

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 28 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 28 + 1.5625

Combine like terms: 28 + 1.5625 = 29.5625
1.5625 + 2.5x + x2 = 29.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 29.5625

Calculate the square root of the right side: 5.437140793

Break this problem into two subproblems by setting 
(x + 1.25) equal to 5.437140793 and -5.437140793.

Subproblem 1

x + 1.25 = 5.437140793 Simplifying x + 1.25 = 5.437140793 Reorder the terms: 1.25 + x = 5.437140793 Solving 1.25 + x = 5.437140793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 5.437140793 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 5.437140793 + -1.25 x = 5.437140793 + -1.25 Combine like terms: 5.437140793 + -1.25 = 4.187140793 x = 4.187140793 Simplifying x = 4.187140793

Subproblem 2

x + 1.25 = -5.437140793 Simplifying x + 1.25 = -5.437140793 Reorder the terms: 1.25 + x = -5.437140793 Solving 1.25 + x = -5.437140793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -5.437140793 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -5.437140793 + -1.25 x = -5.437140793 + -1.25 Combine like terms: -5.437140793 + -1.25 = -6.687140793 x = -6.687140793 Simplifying x = -6.687140793

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.187140793, -6.687140793}

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