Solve x2 = 78 by inspection. There are two real solutions. Enter the lesser number first, and use exponents in your responses.
Solve the following quadratic equation using square roots: -9+(x-3)^2/-4 =- 4.
• {28,-22}
• {8,-2}
• {2,-8}
• {16,-10}
x^2 = 78
Taking the square root of both sides:
x = ±√78
Using a calculator, we can determine the square root of 78 to be approximately 8.831.
Therefore, the two real solutions are:
x = -8.831, 8.831
-9+(x-3)^2/-4 = -4
To start, we can first multiply both sides by -4 to eliminate the fraction:
-4(-9+(x-3)^2/-4) = -4(-4)
36-(x-3)^2 = 16
Next, we can rearrange the equation to isolate the square term:
(x-3)^2 = 36-16
(x-3)^2 = 20
Taking the square root of both sides:
x-3 = ±√20
Simplifying the square root of 20 to √4 * √5 = 2√5
x-3 = ±2√5
Now we can solve for x by adding 3 to both sides:
x = 3 ± 2√5
Therefore, the two real solutions are:
x = 3 + 2√5, 3 - 2√5