13-13X=(4X+3)(X+1)

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Solution for 13-13X=(4X+3)(X+1) equation:


Simplifying
13 + -13X = (4X + 3)(X + 1)

Reorder the terms:
13 + -13X = (3 + 4X)(X + 1)

Reorder the terms:
13 + -13X = (3 + 4X)(1 + X)

Multiply (3 + 4X) * (1 + X)
13 + -13X = (3(1 + X) + 4X * (1 + X))
13 + -13X = ((1 * 3 + X * 3) + 4X * (1 + X))
13 + -13X = ((3 + 3X) + 4X * (1 + X))
13 + -13X = (3 + 3X + (1 * 4X + X * 4X))
13 + -13X = (3 + 3X + (4X + 4X2))

Combine like terms: 3X + 4X = 7X
13 + -13X = (3 + 7X + 4X2)

Solving
13 + -13X = 3 + 7X + 4X2

Solving for variable 'X'.

Reorder the terms:
13 + -3 + -13X + -7X + -4X2 = 3 + 7X + 4X2 + -3 + -7X + -4X2

Combine like terms: 13 + -3 = 10
10 + -13X + -7X + -4X2 = 3 + 7X + 4X2 + -3 + -7X + -4X2

Combine like terms: -13X + -7X = -20X
10 + -20X + -4X2 = 3 + 7X + 4X2 + -3 + -7X + -4X2

Reorder the terms:
10 + -20X + -4X2 = 3 + -3 + 7X + -7X + 4X2 + -4X2

Combine like terms: 3 + -3 = 0
10 + -20X + -4X2 = 0 + 7X + -7X + 4X2 + -4X2
10 + -20X + -4X2 = 7X + -7X + 4X2 + -4X2

Combine like terms: 7X + -7X = 0
10 + -20X + -4X2 = 0 + 4X2 + -4X2
10 + -20X + -4X2 = 4X2 + -4X2

Combine like terms: 4X2 + -4X2 = 0
10 + -20X + -4X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -10X + -2X2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + -10X + -2X2)' equal to zero and attempt to solve: Simplifying 5 + -10X + -2X2 = 0 Solving 5 + -10X + -2X2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + 5X + X2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 5X + 2.5 + X2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 5X + X2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 5X + X2 = 0 + 2.5 5X + X2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 5X + X2 = 2.5 The X term is 5X. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5X + 6.25 + X2 = 2.5 + 6.25 Reorder the terms: 6.25 + 5X + X2 = 2.5 + 6.25 Combine like terms: 2.5 + 6.25 = 8.75 6.25 + 5X + X2 = 8.75 Factor a perfect square on the left side: (X + 2.5)(X + 2.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (X + 2.5) equal to 2.958039892 and -2.958039892.

Subproblem 1

X + 2.5 = 2.958039892 Simplifying X + 2.5 = 2.958039892 Reorder the terms: 2.5 + X = 2.958039892 Solving 2.5 + X = 2.958039892 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + X = 2.958039892 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = 2.958039892 + -2.5 X = 2.958039892 + -2.5 Combine like terms: 2.958039892 + -2.5 = 0.458039892 X = 0.458039892 Simplifying X = 0.458039892

Subproblem 2

X + 2.5 = -2.958039892 Simplifying X + 2.5 = -2.958039892 Reorder the terms: 2.5 + X = -2.958039892 Solving 2.5 + X = -2.958039892 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + X = -2.958039892 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = -2.958039892 + -2.5 X = -2.958039892 + -2.5 Combine like terms: -2.958039892 + -2.5 = -5.458039892 X = -5.458039892 Simplifying X = -5.458039892

Solution

The solution to the problem is based on the solutions from the subproblems. X = {0.458039892, -5.458039892}

Solution

X = {0.458039892, -5.458039892}

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