Solve the radical equation 3x−11−−−−−−√+5=x+2 .(1 point) Responses x=4 or x=−5 x equals 4 or x equals negative 5 x=−5 x equals negative 5 x=4 or x=5 x equals 4 or x equals 5 x=4
To solve the equation, let's isolate the radical term on one side of the equation.
Starting with the given equation:
3x - 11√ + 5 = x + 2
First, let's subtract x from both sides:
2x - 11√ + 5 = 2
Next, let's subtract 5 from both sides:
2x - 11√ = -3
Now, let's get rid of the square root on the left side by squaring both sides of the equation:
(2x - 11√)² = (-3)²
Expanding the left side:
4x² - 44x + 121 + 11x² - 22x - 121 = 9
Combining like terms:
15x² - 66x - 9 = 0
Now, we can solve the quadratic equation. However, this quadratic equation does not factor nicely. Therefore, we will use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this case, a = 15, b = -66, and c = -9.
Plugging in these values into the quadratic formula:
x = (-(-66) ± √((-66)² - 4(15)(-9))) / (2(15))
Simplifying:
x = (66 ± √(4356 + 540)) / 30
x = (66 ± √(4896)) / 30
x = (66 ± 69.97) / 30
x ≈ (66 + 69.97) / 30 or x ≈ (66 - 69.97) / 30
x ≈ 4.5323 or x ≈ -0.0997
Rounded to the nearest whole number, x is approximately equal to 5 or x is approximately equal to 0. Therefore, the correct response is:
x equals 5 or x equals 0