Question

Solve for x: −3(x − 2)2 + 17 = 0

Round your answer to the nearest hundredth.

x = 0.38, −4.38
x = 3.67, −7.67
x = 4.38, −0.38
x = 7.67, −3.67

Answer 1

"x = 4.38, −0.38"

Explanation:

The equation to solve is a quadratic:

`-3(x-2)^(2)+17=0`

We take -17 to the other side and divide by -3 and solve by taking square root and be sure to take + and - solutions:

`-3(x-2)^(2)+17=0\\-3(x-2)^(2)=-17\\(x-2)^(2)=5.67\\x-2=+-√(5.67) \\x-2=+-2.38\\x=2.38+2=4.38\\x=-2.38+2=-0.38`

Hence, the solutions are x = 4.38 and -0.38