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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Identify all of the following solutions of square root of x plus 10 end root minus 4 equals x.
Solution:
Given: Square root of x plus 10 end root minus 4 equals x
It can be mathematically written as
√(x + 10) - 4 = x
√(x + 10) = x + 4
By squaring on both sides
(x + 10) = (x + 4)2
Let us expand it using the algebraic identity (a + b)2 = a2 + b2 + 2ab
x + 10 = x2 + 8x + 16
x2 + 7x + 6 = 0
By splitting the middle term
x2 + x + 6x + 6 = 0
Taking out the common terms
x(x + 1) + 6(x + 1) = 0
(x + 1)(x + 6) = 0
x = -1 or x = -6
Let us substitute x = -6 in the equation
√(-6 + 10) - 4 = √4 - 4 = 2 - 4 ≠ -6
x = -6 is an extraneous solution.
Therefore, the solution is x = -1.
Identify all of the following solutions of square root of x plus 10 end root minus 4 equals x.
Summary:
The solution of the square root of x plus 10 end root minus 4 equals x is x = -1.
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