give exact and approximate solutions to three decimal places
(x-5)sq = 18
If you mean (x-5)^2 = 18,
x-5 = +or- sqrt18 = +or- 4.243
x = 0.757 or 9.243
To find the exact and approximate solutions to the equation (x-5)^2 = 18, we need to solve for x.
Step 1: Expand the equation:
x^2 - 10x + 25 = 18
Step 2: Move all terms to one side to set the equation equal to zero:
x^2 - 10x + 7 = 0
Step 3: Use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a
For our equation, a = 1, b = -10, and c = 7.
x = (-(-10) ± √((-10)^2 - 4(1)(7))) / (2(1))
x = (10 ± √(100 - 28)) / 2
x = (10 ± √72) / 2
x = (10 ± 8.485) / 2
Step 4: Simplify the solutions:
x1 = (10 + 8.485) / 2 = 9.242
x2 = (10 - 8.485) / 2 = 1.758
Therefore, the exact solutions to the equation (x-5)^2 = 18 are approximately x = 9.242 and x = 1.758, when rounded to three decimal places.
To find the exact and approximate solutions to the equation (x - 5)^2 = 18, we can follow these steps:
Step 1: Expand the equation:
(x - 5)^2 = 18
x^2 - 10x + 25 = 18
Step 2: Subtract 18 from both sides:
x^2 - 10x + 25 - 18 = 0
x^2 - 10x + 7 = 0
Now we have a quadratic equation in standard form: ax^2 + bx + c = 0, where:
a = 1
b = -10
c = 7
Step 3: Solve the quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values, we get:
x = (-(-10) ± √((-10)^2 - 4(1)(7))) / (2(1))
x = (10 ± √(100 - 28)) / 2
x = (10 ± √72) / 2
x = (10 ± 8.485) / 2
Step 4: Calculate the two possible solutions:
x1 = (10 + 8.485) / 2
x1 = 18.485 / 2
x1 = 9.243
x2 = (10 - 8.485) / 2
x2 = 1.515 / 2
x2 = 0.758
Therefore, the exact solutions to the equation (x - 5)^2 = 18 are x = 9.243 and x = 0.758, rounded to three decimal places.