Give exact and approximate solutions to three decimal places.
(x-8)^2=49
I need step by step example on how to solve this AND input it into a calculator. Please!
You should not need a calculator for this. Use your head.
Take the square root of both sides.
x - 8 equals +7 or -7.
x = 15 or 1.
Give exact and approximate solutions to three decimal places.
y^2-6y+9=25
x^2+5x-7=0
To solve the equation (x-8)^2 = 49, you need to take the square root of both sides of the equation, then solve for x.
Step-by-step solution:
1. Take the square root of both sides of the equation:
√((x-8)^2) = √(49)
|x-8| = 7
2. Set up the two possible cases:
Case 1: x-8 = 7
Case 2: x-8 = -7
Solve each case separately.
Case 1:
3. Solve for x in the first case by adding 8 to both sides:
x - 8 = 7
x = 7 + 8
x = 15
Case 2:
4. Solve for x in the second case by subtracting 8 from both sides:
x - 8 = -7
x = -7 + 8
x = 1
So the exact solutions to the equation (x-8)^2 = 49 are x = 15 and x = 1.
Approximate solutions to three decimal places:
To input this equation into a calculator, you can represent (x-8)^2 as (x-8)^2 - 49 = 0. Then use the quadratic formula or graphing calculator to find the approximate solutions.
Using a calculator:
1. Enter the equation as (x-8)^2 - 49 = 0.
2. Use the solve or zero function on the calculator to find the x-intercepts or roots.
Approximate solutions: x ≈ 15 and x ≈ 1.
So the approximate solutions to the equation (x-8)^2 = 49 are x ≈ 15 and x ≈ 1, rounded to three decimal places.