(3x+14)(x+1)=10

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Solution for (3x+14)(x+1)=10 equation:


Simplifying
(3x + 14)(x + 1) = 10

Reorder the terms:
(14 + 3x)(x + 1) = 10

Reorder the terms:
(14 + 3x)(1 + x) = 10

Multiply (14 + 3x) * (1 + x)
(14(1 + x) + 3x * (1 + x)) = 10
((1 * 14 + x * 14) + 3x * (1 + x)) = 10
((14 + 14x) + 3x * (1 + x)) = 10
(14 + 14x + (1 * 3x + x * 3x)) = 10
(14 + 14x + (3x + 3x2)) = 10

Combine like terms: 14x + 3x = 17x
(14 + 17x + 3x2) = 10

Solving
14 + 17x + 3x2 = 10

Solving for variable 'x'.

Reorder the terms:
14 + -10 + 17x + 3x2 = 10 + -10

Combine like terms: 14 + -10 = 4
4 + 17x + 3x2 = 10 + -10

Combine like terms: 10 + -10 = 0
4 + 17x + 3x2 = 0

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

Divide each side by '3'.
1.333333333 + 5.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 5.666666667x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 5.666666667x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 5.666666667x + x2 = 0 + -1.333333333
5.666666667x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
5.666666667x + x2 = -1.333333333

The x term is 5.666666667x.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667x + 8.027777782 + x2 = -1.333333333 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667x + x2 = -1.333333333 + 8.027777782

Combine like terms: -1.333333333 + 8.027777782 = 6.694444449
8.027777782 + 5.666666667x + x2 = 6.694444449

Factor a perfect square on the left side:
(x + 2.833333334)(x + 2.833333334) = 6.694444449

Calculate the square root of the right side: 2.58736245

Break this problem into two subproblems by setting 
(x + 2.833333334) equal to 2.58736245 and -2.58736245.

Subproblem 1

x + 2.833333334 = 2.58736245 Simplifying x + 2.833333334 = 2.58736245 Reorder the terms: 2.833333334 + x = 2.58736245 Solving 2.833333334 + x = 2.58736245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = 2.58736245 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 2.58736245 + -2.833333334 x = 2.58736245 + -2.833333334 Combine like terms: 2.58736245 + -2.833333334 = -0.245970884 x = -0.245970884 Simplifying x = -0.245970884

Subproblem 2

x + 2.833333334 = -2.58736245 Simplifying x + 2.833333334 = -2.58736245 Reorder the terms: 2.833333334 + x = -2.58736245 Solving 2.833333334 + x = -2.58736245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = -2.58736245 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -2.58736245 + -2.833333334 x = -2.58736245 + -2.833333334 Combine like terms: -2.58736245 + -2.833333334 = -5.420695784 x = -5.420695784 Simplifying x = -5.420695784

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.245970884, -5.420695784}

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