Answer:
The number is 6.
Step-by-step explanation:
106-6=100
100/10=10
10-4=6
To show your work, write that process in reverse.
The number is equal to 5.
In this exercise, you're required to write an algebraic expression and solve for the unknown variable or number.
Translating the word problem into an algebraic expression, we have;
[tex]p^{2} + (p + 4)^2 = 106\\\\p^{2} + p^{2} + 4p + 4p + 16 = 106\\\\2p^{2} + 8p + 16 = 106\\\\2p^{2} + 8p = 106 - 16\\\\2p^{2} + 8p = 90[/tex]
Dividing all through by 2, we have;
[tex]p^{2} + 4p = 45\\\\p^{2} + 4p - 45 = 0[/tex]
Solving the quadratic equation by factorization, we have;
[tex]p^{2} + 9p - 5p - 45 = 0\\\\p(p + 9) - 5(p + 9) = 0\\\\(p + 9)(p - 5) = 0[/tex]
Since the number is a positive number, then p = 5
Therefore, the number is equal to 5.
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