189=(25+4x)(21+2x)-525

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Solution for 189=(25+4x)(21+2x)-525 equation:


Simplifying
189 = (25 + 4x)(21 + 2x) + -525

Multiply (25 + 4x) * (21 + 2x)
189 = (25(21 + 2x) + 4x * (21 + 2x)) + -525
189 = ((21 * 25 + 2x * 25) + 4x * (21 + 2x)) + -525
189 = ((525 + 50x) + 4x * (21 + 2x)) + -525
189 = (525 + 50x + (21 * 4x + 2x * 4x)) + -525
189 = (525 + 50x + (84x + 8x2)) + -525

Combine like terms: 50x + 84x = 134x
189 = (525 + 134x + 8x2) + -525

Reorder the terms:
189 = 525 + -525 + 134x + 8x2

Combine like terms: 525 + -525 = 0
189 = 0 + 134x + 8x2
189 = 134x + 8x2

Solving
189 = 134x + 8x2

Solving for variable 'x'.

Reorder the terms:
189 + -134x + -8x2 = 134x + -134x + 8x2 + -8x2

Combine like terms: 134x + -134x = 0
189 + -134x + -8x2 = 0 + 8x2 + -8x2
189 + -134x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
189 + -134x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-23.625 + 16.75x + x2 = 0

Move the constant term to the right:

Add '23.625' to each side of the equation.
-23.625 + 16.75x + 23.625 + x2 = 0 + 23.625

Reorder the terms:
-23.625 + 23.625 + 16.75x + x2 = 0 + 23.625

Combine like terms: -23.625 + 23.625 = 0.000
0.000 + 16.75x + x2 = 0 + 23.625
16.75x + x2 = 0 + 23.625

Combine like terms: 0 + 23.625 = 23.625
16.75x + x2 = 23.625

The x term is 16.75x.  Take half its coefficient (8.375).
Square it (70.140625) and add it to both sides.

Add '70.140625' to each side of the equation.
16.75x + 70.140625 + x2 = 23.625 + 70.140625

Reorder the terms:
70.140625 + 16.75x + x2 = 23.625 + 70.140625

Combine like terms: 23.625 + 70.140625 = 93.765625
70.140625 + 16.75x + x2 = 93.765625

Factor a perfect square on the left side:
(x + 8.375)(x + 8.375) = 93.765625

Calculate the square root of the right side: 9.683265203

Break this problem into two subproblems by setting 
(x + 8.375) equal to 9.683265203 and -9.683265203.

Subproblem 1

x + 8.375 = 9.683265203 Simplifying x + 8.375 = 9.683265203 Reorder the terms: 8.375 + x = 9.683265203 Solving 8.375 + x = 9.683265203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.375' to each side of the equation. 8.375 + -8.375 + x = 9.683265203 + -8.375 Combine like terms: 8.375 + -8.375 = 0.000 0.000 + x = 9.683265203 + -8.375 x = 9.683265203 + -8.375 Combine like terms: 9.683265203 + -8.375 = 1.308265203 x = 1.308265203 Simplifying x = 1.308265203

Subproblem 2

x + 8.375 = -9.683265203 Simplifying x + 8.375 = -9.683265203 Reorder the terms: 8.375 + x = -9.683265203 Solving 8.375 + x = -9.683265203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.375' to each side of the equation. 8.375 + -8.375 + x = -9.683265203 + -8.375 Combine like terms: 8.375 + -8.375 = 0.000 0.000 + x = -9.683265203 + -8.375 x = -9.683265203 + -8.375 Combine like terms: -9.683265203 + -8.375 = -18.058265203 x = -18.058265203 Simplifying x = -18.058265203

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.308265203, -18.058265203}

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