Solve for X: 3x+7+3x+5-x = 3(x-3)(x+3)+5x Linear-Quadratic Equation

Question

Solve the following equation:

_{^{$3x+7+3x+5-x=3(x-3)(x+3)+5x$}}

00:00 Solve

00:03 Collect terms

00:23 Use abbreviated multiplication formulas

00:40 Reduce what's possible

00:47 Divide by 3

01:02 Arrange the exercise so that 0 is on one side of the equation

01:15 Break down 13 into square root of 13 squared

01:18 Again use abbreviated multiplication formulas to find solutions

01:26 Find the two possible solutions

01:41 And this is the solution to the question

To solve this problem, let's follow these steps:

Step 1: Simplify the left-hand side of the equation:
Combine like terms: $3x + 3x - x + 7 + 5 = 5x + 12$ .
Step 2: Expand and simplify the right-hand side:
Apply the difference of squares: $3(x-3)(x+3) = 3(x^2 - 9)$ .
This simplifies to $3x^2 - 27$ .
Then add $5x$ : $3x^2 - 27 + 5x$ .
Step 3: Equate both sides and solve for $x$ :
We have $5x + 12 = 3x^2 + 5x - 27$ .
Subtract $5x$ and 12 from both sides: $0 = 3x^2 - 39$ .
This simplifies to $3x^2 = 39$ .
Divide by 3: $x^2 = 13$ .
Taking the square root of both sides, we find $x = \pm\sqrt{13}$ .

Therefore, the solution to the equation is $x = \pm\sqrt{13}$ .

$±\sqrt{13}$