4x^2+21x-18=-8x+9

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Solution for 4x^2+21x-18=-8x+9 equation:


Simplifying
4x2 + 21x + -18 = -8x + 9

Reorder the terms:
-18 + 21x + 4x2 = -8x + 9

Reorder the terms:
-18 + 21x + 4x2 = 9 + -8x

Solving
-18 + 21x + 4x2 = 9 + -8x

Solving for variable 'x'.

Reorder the terms:
-18 + -9 + 21x + 8x + 4x2 = 9 + -8x + -9 + 8x

Combine like terms: -18 + -9 = -27
-27 + 21x + 8x + 4x2 = 9 + -8x + -9 + 8x

Combine like terms: 21x + 8x = 29x
-27 + 29x + 4x2 = 9 + -8x + -9 + 8x

Reorder the terms:
-27 + 29x + 4x2 = 9 + -9 + -8x + 8x

Combine like terms: 9 + -9 = 0
-27 + 29x + 4x2 = 0 + -8x + 8x
-27 + 29x + 4x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-27 + 29x + 4x2 = 0

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

Divide each side by '4'.
-6.75 + 7.25x + x2 = 0

Move the constant term to the right:

Add '6.75' to each side of the equation.
-6.75 + 7.25x + 6.75 + x2 = 0 + 6.75

Reorder the terms:
-6.75 + 6.75 + 7.25x + x2 = 0 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + 7.25x + x2 = 0 + 6.75
7.25x + x2 = 0 + 6.75

Combine like terms: 0 + 6.75 = 6.75
7.25x + x2 = 6.75

The x term is 7.25x.  Take half its coefficient (3.625).
Square it (13.140625) and add it to both sides.

Add '13.140625' to each side of the equation.
7.25x + 13.140625 + x2 = 6.75 + 13.140625

Reorder the terms:
13.140625 + 7.25x + x2 = 6.75 + 13.140625

Combine like terms: 6.75 + 13.140625 = 19.890625
13.140625 + 7.25x + x2 = 19.890625

Factor a perfect square on the left side:
(x + 3.625)(x + 3.625) = 19.890625

Calculate the square root of the right side: 4.459890694

Break this problem into two subproblems by setting 
(x + 3.625) equal to 4.459890694 and -4.459890694.

Subproblem 1

x + 3.625 = 4.459890694 Simplifying x + 3.625 = 4.459890694 Reorder the terms: 3.625 + x = 4.459890694 Solving 3.625 + x = 4.459890694 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = 4.459890694 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = 4.459890694 + -3.625 x = 4.459890694 + -3.625 Combine like terms: 4.459890694 + -3.625 = 0.834890694 x = 0.834890694 Simplifying x = 0.834890694

Subproblem 2

x + 3.625 = -4.459890694 Simplifying x + 3.625 = -4.459890694 Reorder the terms: 3.625 + x = -4.459890694 Solving 3.625 + x = -4.459890694 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = -4.459890694 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = -4.459890694 + -3.625 x = -4.459890694 + -3.625 Combine like terms: -4.459890694 + -3.625 = -8.084890694 x = -8.084890694 Simplifying x = -8.084890694

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.834890694, -8.084890694}

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