(2x+3)(x-14)=-14

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Solution for (2x+3)(x-14)=-14 equation:


Simplifying
(2x + 3)(x + -14) = -14

Reorder the terms:
(3 + 2x)(x + -14) = -14

Reorder the terms:
(3 + 2x)(-14 + x) = -14

Multiply (3 + 2x) * (-14 + x)
(3(-14 + x) + 2x * (-14 + x)) = -14
((-14 * 3 + x * 3) + 2x * (-14 + x)) = -14
((-42 + 3x) + 2x * (-14 + x)) = -14
(-42 + 3x + (-14 * 2x + x * 2x)) = -14
(-42 + 3x + (-28x + 2x2)) = -14

Combine like terms: 3x + -28x = -25x
(-42 + -25x + 2x2) = -14

Solving
-42 + -25x + 2x2 = -14

Solving for variable 'x'.

Reorder the terms:
-42 + 14 + -25x + 2x2 = -14 + 14

Combine like terms: -42 + 14 = -28
-28 + -25x + 2x2 = -14 + 14

Combine like terms: -14 + 14 = 0
-28 + -25x + 2x2 = 0

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

Divide each side by '2'.
-14 + -12.5x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -12.5x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -12.5x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -12.5x + x2 = 0 + 14
-12.5x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-12.5x + x2 = 14

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = 14 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = 14 + 39.0625

Combine like terms: 14 + 39.0625 = 53.0625
39.0625 + -12.5x + x2 = 53.0625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 53.0625

Calculate the square root of the right side: 7.284401142

Break this problem into two subproblems by setting 
(x + -6.25) equal to 7.284401142 and -7.284401142.

Subproblem 1

x + -6.25 = 7.284401142 Simplifying x + -6.25 = 7.284401142 Reorder the terms: -6.25 + x = 7.284401142 Solving -6.25 + x = 7.284401142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 7.284401142 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 7.284401142 + 6.25 x = 7.284401142 + 6.25 Combine like terms: 7.284401142 + 6.25 = 13.534401142 x = 13.534401142 Simplifying x = 13.534401142

Subproblem 2

x + -6.25 = -7.284401142 Simplifying x + -6.25 = -7.284401142 Reorder the terms: -6.25 + x = -7.284401142 Solving -6.25 + x = -7.284401142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -7.284401142 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -7.284401142 + 6.25 x = -7.284401142 + 6.25 Combine like terms: -7.284401142 + 6.25 = -1.034401142 x = -1.034401142 Simplifying x = -1.034401142

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.534401142, -1.034401142}

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