2 root3 = square root of xsquared + 5x
To solve the equation 2√3 = √(x^2 + 5x), we need to isolate the variable x.
1. Start by squaring both sides of the equation to eliminate the square root symbol:
(2√3)^2 = (√(x^2 + 5x))^2
4 * 3 = x^2 + 5x
12 = x^2 + 5x
2. Rearrange the equation into standard quadratic form:
x^2 + 5x - 12 = 0
3. Now, we need to factor or use the quadratic formula to solve for x.
Factoring: Find two numbers that multiply to -12 and add up to 5. The numbers are 8 and -3.
(x + 8)(x - 3) = 0
Set each factor to zero and solve for x:
x + 8 = 0 or x - 3 = 0
If we solve each equation separately:
x + 8 = 0 => x = -8
x - 3 = 0 => x = 3
Therefore, the solutions to the equation 2√3 = √(x^2 + 5x) are x = -8 and x = 3.