Solve the Equation: Unravel the Quadratic (x+3)² + (2x-3)² = 5x(x-3/5)

Find a X given the following equation:

$(x+3)^2+(2x-3)^2=5x(x-\frac{3}{5})$

Video Solution

Solution Steps

00:11 Let's find the value of X.

00:21 First, use the shortcut multiplication formulas. Open the parentheses step by step.

00:37 Carefully multiply each term inside the parentheses with factors outside.

01:02 Now, solve all the multiplications and calculate the squares.

01:17 Next, group the terms that are similar together.

01:47 Then, isolate the variable X to find its value.

02:19 And that's how we find the solution. Great work!

Step-by-Step Solution

To solve this problem, let's expand and simplify each side of the given equation:

Step 1: Expand the left side:
- Expand $(x + 3)^2 = x^2 + 6x + 9$
- Expand $(2x - 3)^2 = 4x^2 - 12x + 9$
Combine them to get $x^2 + 6x + 9 + 4x^2 - 12x + 9 = 5x^2 - 6x + 18$ .
Step 2: Expand the right side:
- Expand $5x(x - \frac{3}{5}) = 5x^2 - 3x$
Step 3: Set the equations from both sides equal and simplify: $5x^2 - 6x + 18 = 5x^2 - 3x$
Step 4: Subtract $5x^2$ from both sides: $-6x + 18 = -3x$
Step 5: Simplify to: $-6x + 3x = -18$ or equivalently $-3x = -18$
Step 6: Solve for $x$ : $x = \frac{-18}{-3} = 6$

Therefore, the solution to the problem is $x = 6$ .