Donte used mental math to find the exact sum of 386 and 14. Which strategy could Donte have used?
2 answers:
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Let be the two numbers. We have two pieces of information:
(the difference between the two numbers is 2)
(their product is 224)
From the first equation, we can deduce
If we plug this expression in the second equation, we have
If you solve this equation with the usual quadratic formula you get the solutions
So, you have the following couple of solutions, recalling that x is 2 more than y:
Answer:
x ≈ 1.32, x ≈ - 5.32
Step-by-step explanation:
Given
x² + 4x - 7 = 0 ( add 7 to both sides )
x² + 4x = 7
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(2)x + 4 = 7 + 4
(x + 2)² = 11 ( take the square root of both sides )
x + 2 = ± ( subtract 2 from both sides )
x = - 2 ±
Thus
x = - 2 - ≈ - 5.32 ( to 2 dec. places )
x = - 2 + ≈ 1.32 ( to 2 dec. places )