[(2x+25)(2x+13)]-(25*13)=160

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Solution for [(2x+25)(2x+13)]-(25*13)=160 equation:


Simplifying
[(2x + 25)(2x + 13)] + -1(25 * 13) = 160

Reorder the terms:
[(25 + 2x)(2x + 13)] + -1(25 * 13) = 160

Reorder the terms:
[(25 + 2x)(13 + 2x)] + -1(25 * 13) = 160

Multiply (25 + 2x) * (13 + 2x)
[(25(13 + 2x) + 2x * (13 + 2x))] + -1(25 * 13) = 160
[((13 * 25 + 2x * 25) + 2x * (13 + 2x))] + -1(25 * 13) = 160
[((325 + 50x) + 2x * (13 + 2x))] + -1(25 * 13) = 160
[(325 + 50x + (13 * 2x + 2x * 2x))] + -1(25 * 13) = 160
[(325 + 50x + (26x + 4x2))] + -1(25 * 13) = 160

Combine like terms: 50x + 26x = 76x
[(325 + 76x + 4x2)] + -1(25 * 13) = 160
[325 + 76x + 4x2] + -1(25 * 13) = 160

Remove brackets around [325 + 76x + 4x2]
325 + 76x + 4x2 + -1(25 * 13) = 160

Multiply 25 * 13
325 + 76x + 4x2 + -1(325) = 160

Multiply -1 * 325
325 + 76x + 4x2 + -325 = 160

Reorder the terms:
325 + -325 + 76x + 4x2 = 160

Combine like terms: 325 + -325 = 0
0 + 76x + 4x2 = 160
76x + 4x2 = 160

Solving
76x + 4x2 = 160

Solving for variable 'x'.

Reorder the terms:
-160 + 76x + 4x2 = 160 + -160

Combine like terms: 160 + -160 = 0
-160 + 76x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-40 + 19x + x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-40 + 19x + x2)' equal to zero and attempt to solve: Simplifying -40 + 19x + x2 = 0 Solving -40 + 19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 19x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 19x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 19x + x2 = 0 + 40 19x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 19x + x2 = 40 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 40 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 40 + 90.25 Combine like terms: 40 + 90.25 = 130.25 90.25 + 19x + x2 = 130.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (x + 9.5) equal to 11.412712211 and -11.412712211.

Subproblem 1

x + 9.5 = 11.412712211 Simplifying x + 9.5 = 11.412712211 Reorder the terms: 9.5 + x = 11.412712211 Solving 9.5 + x = 11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 11.412712211 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 11.412712211 + -9.5 x = 11.412712211 + -9.5 Combine like terms: 11.412712211 + -9.5 = 1.912712211 x = 1.912712211 Simplifying x = 1.912712211

Subproblem 2

x + 9.5 = -11.412712211 Simplifying x + 9.5 = -11.412712211 Reorder the terms: 9.5 + x = -11.412712211 Solving 9.5 + x = -11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -11.412712211 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -11.412712211 + -9.5 x = -11.412712211 + -9.5 Combine like terms: -11.412712211 + -9.5 = -20.912712211 x = -20.912712211 Simplifying x = -20.912712211

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.912712211, -20.912712211}

Solution

x = {1.912712211, -20.912712211}

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