Answer:
14 years old
Step-by-step explanation:
<u>Define the variable</u>
Let x be the actual age of Zeba (in years).
<u>Create an equation</u> using the give information and the variable x:
![(x - 5)^2=5x+11](https://tex.z-dn.net/?f=%28x%20-%205%29%5E2%3D5x%2B11)
To find Zeba's age now, <u>solve the equation for x</u>.
Expand the brackets:
![\implies x^2-10x+25=5x+11](https://tex.z-dn.net/?f=%5Cimplies%20x%5E2-10x%2B25%3D5x%2B11)
Subtract 5x from both sides:
![\implies x^2-10x+25-5x=5x+11-5x](https://tex.z-dn.net/?f=%5Cimplies%20x%5E2-10x%2B25-5x%3D5x%2B11-5x)
![\implies x^2-15x+25=11](https://tex.z-dn.net/?f=%5Cimplies%20x%5E2-15x%2B25%3D11)
Subtract 11 from both sides:
![\implies x^2-15x+25-11=11-11](https://tex.z-dn.net/?f=%5Cimplies%20x%5E2-15x%2B25-11%3D11-11)
![\implies x^2-15x+14=0](https://tex.z-dn.net/?f=%5Cimplies%20x%5E2-15x%2B14%3D0)
<u>Factor the found quadratic</u>
To factor a quadratic in the form
<em>, </em>find two numbers that multiply to
and sum to
, then rewrite
as the sum of these two numbers:
![\implies x^2-14x-x+14=0](https://tex.z-dn.net/?f=%5Cimplies%20x%5E2-14x-x%2B14%3D0)
Factor the first two terms and the last two terms separately:
![\implies x(x-14)-1(x-14)=0](https://tex.z-dn.net/?f=%5Cimplies%20x%28x-14%29-1%28x-14%29%3D0)
Factor out the common term (x - 14):
![\implies (x-1)(x-14)=0](https://tex.z-dn.net/?f=%5Cimplies%20%28x-1%29%28x-14%29%3D0)
Apply the <u>zero product property</u>:
![\implies (x-1)=0 \implies x=1](https://tex.z-dn.net/?f=%5Cimplies%20%28x-1%29%3D0%20%5Cimplies%20x%3D1)
![\implies (x-14)=0 \implies x=14](https://tex.z-dn.net/?f=%5Cimplies%20%28x-14%29%3D0%20%5Cimplies%20x%3D14)
Therefore, Zeba's age now is either 1 or 14 years.
As the question states "If Zeba were younger by 5 years" then 1 must be an <u>extraneous solution</u> since 1 - 5 = -4 and Zeba cannot be -4 years old.
Therefore, Zeba's age now is 14 years old.
<u>Check</u>
Given the actual age of Zeba is 14 years old.
Therefore, If Zeba were younger by 5 years, she would be 9 years old as: 14 - 5 = 9
The square of 9 is: 9² = 81.
5 times her actual age: 5 × 14 = 70
81 is 11 more than 70, hence verifying that her <u>actual age is 14 years old</u>.
Learn more about quadratic equations here:
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