(3x+4)(x+7)-18=

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Solution for (3x+4)(x+7)-18= equation:


Simplifying
(3x + 4)(x + 7) + -18 = 0

Reorder the terms:
(4 + 3x)(x + 7) + -18 = 0

Reorder the terms:
(4 + 3x)(7 + x) + -18 = 0

Multiply (4 + 3x) * (7 + x)
(4(7 + x) + 3x * (7 + x)) + -18 = 0
((7 * 4 + x * 4) + 3x * (7 + x)) + -18 = 0
((28 + 4x) + 3x * (7 + x)) + -18 = 0
(28 + 4x + (7 * 3x + x * 3x)) + -18 = 0
(28 + 4x + (21x + 3x2)) + -18 = 0

Combine like terms: 4x + 21x = 25x
(28 + 25x + 3x2) + -18 = 0

Reorder the terms:
28 + -18 + 25x + 3x2 = 0

Combine like terms: 28 + -18 = 10
10 + 25x + 3x2 = 0

Solving
10 + 25x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
3.333333333 + 8.333333333x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + 8.333333333x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + 8.333333333x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + 8.333333333x + x2 = 0 + -3.333333333
8.333333333x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
8.333333333x + x2 = -3.333333333

The x term is 8.333333333x.  Take half its coefficient (4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
8.333333333x + 17.36111111 + x2 = -3.333333333 + 17.36111111

Reorder the terms:
17.36111111 + 8.333333333x + x2 = -3.333333333 + 17.36111111

Combine like terms: -3.333333333 + 17.36111111 = 14.027777777
17.36111111 + 8.333333333x + x2 = 14.027777777

Factor a perfect square on the left side:
(x + 4.166666667)(x + 4.166666667) = 14.027777777

Calculate the square root of the right side: 3.745367509

Break this problem into two subproblems by setting 
(x + 4.166666667) equal to 3.745367509 and -3.745367509.

Subproblem 1

x + 4.166666667 = 3.745367509 Simplifying x + 4.166666667 = 3.745367509 Reorder the terms: 4.166666667 + x = 3.745367509 Solving 4.166666667 + x = 3.745367509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = 3.745367509 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = 3.745367509 + -4.166666667 x = 3.745367509 + -4.166666667 Combine like terms: 3.745367509 + -4.166666667 = -0.421299158 x = -0.421299158 Simplifying x = -0.421299158

Subproblem 2

x + 4.166666667 = -3.745367509 Simplifying x + 4.166666667 = -3.745367509 Reorder the terms: 4.166666667 + x = -3.745367509 Solving 4.166666667 + x = -3.745367509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = -3.745367509 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = -3.745367509 + -4.166666667 x = -3.745367509 + -4.166666667 Combine like terms: -3.745367509 + -4.166666667 = -7.912034176 x = -7.912034176 Simplifying x = -7.912034176

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.421299158, -7.912034176}

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