Question

Solve the equation x²−18x=17 using complete the square.

a) x = 9 ± √26
b) x = -9 ± √26
c) x = 9 ± √35
d) x = -9 ± √35

Answer 1

To solve the quadratic equation x² - 18x = 17, let’s complete the square:

Start by adding 17 to both sides of the equation: [ x^2 - 18x + 17 = 0 ]

Now, we’ll focus on the quadratic term (the (x^2) term) and the linear term (the (x) term): [ x^2 - 18x = -17 ]

To complete the square, take half of the coefficient of the linear term ((-18)) and square it: [ \left(\frac{-18}{2}\right)^2 = 81 ]

Add 81 to both sides of the equation: [ x^2 - 18x + 81 = 64 ]

Rewrite the left side as a perfect square: [ (x - 9)^2 = 64 ]

Take the square root of both sides: [ x - 9 = \pm 8 ]

Solve for x:

If (x - 9 = 8), then (x = 17).

If (x - 9 = -8), then (x = 1).

Therefore, the solutions are:

(x = 17)

(x = 1)

The correct answers are:

a) (x = 9 \pm \sqrt{26})

b) (x = -9 \pm \sqrt{26})

Step-by-step explanation:

Answer 2

To solve the equation x²−18x=17 using complete the square, rearrange the equation, complete the square by adding the square of half the coefficient of x to both sides, simplify, take the square root, and solve for x.

Step-by-step explanation:

To solve the equation x²−18x=17 using complete the square, we need to rearrange the equation to make the coefficient of x² equal to 1. Start by subtracting 17 from both sides to get x²−18x-17=0. Now, to complete the square, add the square of half of the coefficient of x to both sides. In this case, the coefficient of x is -18, so add (18/2)² = 9² = 81 to both sides. This gives us x²−18x+81-17=81. Simplifying this equation, we get (x-9)²=81. Taking the square root of both sides, we have x-9= ±√81, which simplifies to x-9= ±9. Finally, solve for x by adding 9 to both sides, giving us x = 9 ± 9.

Therefore, the correct answer is option a) x = 9 ± √26.