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Find the smaller value of x that satisfies the equation x2 + 7x + 10 = 0
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x2 + 7x + 10 = 0
The above equation is a quadratic equation and thus, the sum of root = 7 and product of root = 10.
Hence, we look for two numbers, when multiplied gives us 10 and when added gives us 7.
Let the two numbers be 5 and 2.
Replace the sum of root with the two numbers. That is:
x2 + 5x + 2x + 10 = 0
Group the equation into two
(x2 + 5x) + (2x + 10) = 0
factorise out the common term in each groupings
x(x + 5) + 2(x + 5) = 0
(x + 2) (x + 5) = 0
x + 2 = 0 and x + 5 = 0
x = -2 and x = -5
Therefore, the smallest value of x is x = -5
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