How can the quadratic formula be used to solve the equation √(8x+7) = 5?
A. Solve for x and give the exact values for x
B. Solve for x as an approximate decimal value, rounding to the nearest hundredth
C. Complete the square to solve for x
D. Use the zero-product property to solve for x
To solve the equation √(8x+7) = 5, you can use the quadratic formula. However, it is important to note that the quadratic formula is typically used to solve quadratic equations in the form ax^2 + bx + c = 0, whereas the given equation is not in this form. So, using the quadratic formula directly in this case may not be the most efficient approach.
To solve the equation √(8x+7) = 5, we can follow these steps:
1. Start by isolating the square root term. Square both sides of the equation to eliminate the square root:
(√(8x+7))^2 = 5^2
8x + 7 = 25
2. Now we have a linear equation. Substract 7 from both sides to isolate the variable x:
8x = 25 - 7
8x = 18
3. Divide both sides by 8 to solve for x:
x = 18/8
x = 9/4
So, the solution to the equation is x = 9/4.
Given the available options, the correct choice for solving this equation would be A. Solve for x and give the exact values for x.
The correct answer is C. Complete the square to solve for x.
To solve the equation √(8x+7) = 5 using the quadratic formula, we can follow these steps:
Step 1: Square both sides of the equation to eliminate the square root:
(√(8x+7))^2 = 5^2
8x + 7 = 25
Step 2: Subtract 7 from both sides of the equation:
8x = 25 - 7
8x = 18
Step 3: Divide both sides of the equation by 8 to solve for x:
x = 18/8
x = 9/4
Therefore, the equation √(8x+7) = 5 can be solved by completing the square to find that x = 9/4.