(x+4)*(x+14)=30

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Solution for (x+4)*(x+14)=30 equation:


Simplifying
(x + 4)(x + 14) = 30

Reorder the terms:
(4 + x)(x + 14) = 30

Reorder the terms:
(4 + x)(14 + x) = 30

Multiply (4 + x) * (14 + x)
(4(14 + x) + x(14 + x)) = 30
((14 * 4 + x * 4) + x(14 + x)) = 30
((56 + 4x) + x(14 + x)) = 30
(56 + 4x + (14 * x + x * x)) = 30
(56 + 4x + (14x + x2)) = 30

Combine like terms: 4x + 14x = 18x
(56 + 18x + x2) = 30

Solving
56 + 18x + x2 = 30

Solving for variable 'x'.

Reorder the terms:
56 + -30 + 18x + x2 = 30 + -30

Combine like terms: 56 + -30 = 26
26 + 18x + x2 = 30 + -30

Combine like terms: 30 + -30 = 0
26 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + 18x + -26 + x2 = 0 + -26

Reorder the terms:
26 + -26 + 18x + x2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + 18x + x2 = 0 + -26
18x + x2 = 0 + -26

Combine like terms: 0 + -26 = -26
18x + x2 = -26

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -26 + 81

Reorder the terms:
81 + 18x + x2 = -26 + 81

Combine like terms: -26 + 81 = 55
81 + 18x + x2 = 55

Factor a perfect square on the left side:
(x + 9)(x + 9) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(x + 9) equal to 7.416198487 and -7.416198487.

Subproblem 1

x + 9 = 7.416198487 Simplifying x + 9 = 7.416198487 Reorder the terms: 9 + x = 7.416198487 Solving 9 + x = 7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 7.416198487 + -9 Combine like terms: 9 + -9 = 0 0 + x = 7.416198487 + -9 x = 7.416198487 + -9 Combine like terms: 7.416198487 + -9 = -1.583801513 x = -1.583801513 Simplifying x = -1.583801513

Subproblem 2

x + 9 = -7.416198487 Simplifying x + 9 = -7.416198487 Reorder the terms: 9 + x = -7.416198487 Solving 9 + x = -7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -7.416198487 + -9 Combine like terms: 9 + -9 = 0 0 + x = -7.416198487 + -9 x = -7.416198487 + -9 Combine like terms: -7.416198487 + -9 = -16.416198487 x = -16.416198487 Simplifying x = -16.416198487

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.583801513, -16.416198487}

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