Question

Given the equation |x-4| = x² - 6x + 9 , and one solution is approximately x = 1.4 , find the other solution rounded to the nearest tenth.

a) 1.4
b) 2.8
c) 3.6
d) 5.2

Answer 1

The other solution to the given equation, rounded to the nearest tenth, is 3.6.

Step-by-step explanation:

This equation can be solved using the quadratic formula. For an equation of the form ax² + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Given the equation |x-4| = x² - 6x + 9, we can rewrite it as:

x-4 = x² - 6x + 9

Simplifying further:

x² - 7x + 5 = 0

Using the quadratic formula, we can solve for x:

x = (7 ± √(7^2 - 4(1)(5))) / (2(1))

Simplifying the expression under the square root:

x = (7 ± √(49 - 20)) / 2

x = (7 ± √29) / 2

The approximate solutions are x ≈ 3.6 and x ≈ 1.4. The other solution, rounded to the nearest tenth, is 3.6 (c)