2x^2+19x=36

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Solution for 2x^2+19x=36 equation:


Simplifying
2x2 + 19x = 36

Reorder the terms:
19x + 2x2 = 36

Solving
19x + 2x2 = 36

Solving for variable 'x'.

Reorder the terms:
-36 + 19x + 2x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 19x + 2x2 = 0

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

Divide each side by '2'.
-18 + 9.5x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 9.5x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 9.5x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 9.5x + x2 = 0 + 18
9.5x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
9.5x + x2 = 18

The x term is 9.5x.  Take half its coefficient (4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
9.5x + 22.5625 + x2 = 18 + 22.5625

Reorder the terms:
22.5625 + 9.5x + x2 = 18 + 22.5625

Combine like terms: 18 + 22.5625 = 40.5625
22.5625 + 9.5x + x2 = 40.5625

Factor a perfect square on the left side:
(x + 4.75)(x + 4.75) = 40.5625

Calculate the square root of the right side: 6.368869601

Break this problem into two subproblems by setting 
(x + 4.75) equal to 6.368869601 and -6.368869601.

Subproblem 1

x + 4.75 = 6.368869601 Simplifying x + 4.75 = 6.368869601 Reorder the terms: 4.75 + x = 6.368869601 Solving 4.75 + x = 6.368869601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 6.368869601 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 6.368869601 + -4.75 x = 6.368869601 + -4.75 Combine like terms: 6.368869601 + -4.75 = 1.618869601 x = 1.618869601 Simplifying x = 1.618869601

Subproblem 2

x + 4.75 = -6.368869601 Simplifying x + 4.75 = -6.368869601 Reorder the terms: 4.75 + x = -6.368869601 Solving 4.75 + x = -6.368869601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -6.368869601 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -6.368869601 + -4.75 x = -6.368869601 + -4.75 Combine like terms: -6.368869601 + -4.75 = -11.118869601 x = -11.118869601 Simplifying x = -11.118869601

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.618869601, -11.118869601}

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