8(x+4)^2= -9
To solve the equation 8(x+4)^2 = -9, you can follow these steps:
Step 1: Divide both sides of the equation by 8 to isolate the square term on the left side:
(x+4)^2 = -9/8
Step 2: Take the square root of both sides to eliminate the square term on the left side. Remember to consider both the positive and negative square roots:
x+4 = ±√(-9/8)
Step 3: Simplify the square root term on the right side. Since -9/8 is a negative number, we can express it with the imaginary unit "i" to represent the square root of -1:
x+4 = ±√(9/8) * i
Step 4: Further simplify the square root term, considering that √(9/8) is the same as √9 / √8, and simplify √9 as 3:
x+4 = ±(3/2) * i√2
Step 5: Move 4 to the right side of the equation to isolate x:
x = -4 ± (3/2) * i√2
Therefore, the solution to the equation 8(x+4)^2 = -9 is x = -4 ± (3/2) * i√2.