4x^2+21x=27

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Solution for 4x^2+21x=27 equation:


Simplifying
4x2 + 21x = 27

Reorder the terms:
21x + 4x2 = 27

Solving
21x + 4x2 = 27

Solving for variable 'x'.

Reorder the terms:
-27 + 21x + 4x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 21x + 4x2 = 0

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

Divide each side by '4'.
-6.75 + 5.25x + x2 = 0

Move the constant term to the right:

Add '6.75' to each side of the equation.
-6.75 + 5.25x + 6.75 + x2 = 0 + 6.75

Reorder the terms:
-6.75 + 6.75 + 5.25x + x2 = 0 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + 5.25x + x2 = 0 + 6.75
5.25x + x2 = 0 + 6.75

Combine like terms: 0 + 6.75 = 6.75
5.25x + x2 = 6.75

The x term is 5.25x.  Take half its coefficient (2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
5.25x + 6.890625 + x2 = 6.75 + 6.890625

Reorder the terms:
6.890625 + 5.25x + x2 = 6.75 + 6.890625

Combine like terms: 6.75 + 6.890625 = 13.640625
6.890625 + 5.25x + x2 = 13.640625

Factor a perfect square on the left side:
(x + 2.625)(x + 2.625) = 13.640625

Calculate the square root of the right side: 3.693321676

Break this problem into two subproblems by setting 
(x + 2.625) equal to 3.693321676 and -3.693321676.

Subproblem 1

x + 2.625 = 3.693321676 Simplifying x + 2.625 = 3.693321676 Reorder the terms: 2.625 + x = 3.693321676 Solving 2.625 + x = 3.693321676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 3.693321676 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 3.693321676 + -2.625 x = 3.693321676 + -2.625 Combine like terms: 3.693321676 + -2.625 = 1.068321676 x = 1.068321676 Simplifying x = 1.068321676

Subproblem 2

x + 2.625 = -3.693321676 Simplifying x + 2.625 = -3.693321676 Reorder the terms: 2.625 + x = -3.693321676 Solving 2.625 + x = -3.693321676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -3.693321676 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -3.693321676 + -2.625 x = -3.693321676 + -2.625 Combine like terms: -3.693321676 + -2.625 = -6.318321676 x = -6.318321676 Simplifying x = -6.318321676

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.068321676, -6.318321676}

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