(x+9)(5x-3)=18

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Solution for (x+9)(5x-3)=18 equation:


Simplifying
(x + 9)(5x + -3) = 18

Reorder the terms:
(9 + x)(5x + -3) = 18

Reorder the terms:
(9 + x)(-3 + 5x) = 18

Multiply (9 + x) * (-3 + 5x)
(9(-3 + 5x) + x(-3 + 5x)) = 18
((-3 * 9 + 5x * 9) + x(-3 + 5x)) = 18
((-27 + 45x) + x(-3 + 5x)) = 18
(-27 + 45x + (-3 * x + 5x * x)) = 18
(-27 + 45x + (-3x + 5x2)) = 18

Combine like terms: 45x + -3x = 42x
(-27 + 42x + 5x2) = 18

Solving
-27 + 42x + 5x2 = 18

Solving for variable 'x'.

Reorder the terms:
-27 + -18 + 42x + 5x2 = 18 + -18

Combine like terms: -27 + -18 = -45
-45 + 42x + 5x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-45 + 42x + 5x2 = 0

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

Divide each side by '5'.
-9 + 8.4x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 8.4x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 8.4x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 8.4x + x2 = 0 + 9
8.4x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
8.4x + x2 = 9

The x term is 8.4x.  Take half its coefficient (4.2).
Square it (17.64) and add it to both sides.

Add '17.64' to each side of the equation.
8.4x + 17.64 + x2 = 9 + 17.64

Reorder the terms:
17.64 + 8.4x + x2 = 9 + 17.64

Combine like terms: 9 + 17.64 = 26.64
17.64 + 8.4x + x2 = 26.64

Factor a perfect square on the left side:
(x + 4.2)(x + 4.2) = 26.64

Calculate the square root of the right side: 5.16139516

Break this problem into two subproblems by setting 
(x + 4.2) equal to 5.16139516 and -5.16139516.

Subproblem 1

x + 4.2 = 5.16139516 Simplifying x + 4.2 = 5.16139516 Reorder the terms: 4.2 + x = 5.16139516 Solving 4.2 + x = 5.16139516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.2' to each side of the equation. 4.2 + -4.2 + x = 5.16139516 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + x = 5.16139516 + -4.2 x = 5.16139516 + -4.2 Combine like terms: 5.16139516 + -4.2 = 0.96139516 x = 0.96139516 Simplifying x = 0.96139516

Subproblem 2

x + 4.2 = -5.16139516 Simplifying x + 4.2 = -5.16139516 Reorder the terms: 4.2 + x = -5.16139516 Solving 4.2 + x = -5.16139516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.2' to each side of the equation. 4.2 + -4.2 + x = -5.16139516 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + x = -5.16139516 + -4.2 x = -5.16139516 + -4.2 Combine like terms: -5.16139516 + -4.2 = -9.36139516 x = -9.36139516 Simplifying x = -9.36139516

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.96139516, -9.36139516}

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